**Subcategory Pollutant**  **No. of Sources**  **Industry wide**  **No. of Sources**  **with Data Determination of No. of** 

**Sources in MA CT Floor**  Floor tile roller kilns Hg 27 7 best performing 5 sources PM 27 10 best performing 5 sources D/F TEQ 27 6 best performing 5 sources Floor tile press dryers DF/TEQ 5 4 best performing 5 sources Floor tile spray dryers DF/TEQ 11 5 best performing 5 sources Wall tile roller kilns Hg 14 1 best performing 5 sources PM 14 1 best performing 5 sources D/F TEQ 14 1 best performing 5 sources Wall tile spray dryers D/F TEQ 5 1 best performing 5 sources Tile glaze lines Hg 24 3 best performing 5 sources PM 24 3 best performing 5 sources First-fire sanitaryware tunnel kilns Hg 11 5 best performing 5 sources PM 11 6 best performing 5 sources D/F TEQ 11 5 best performing 5 sources First-fire sanitaryware manual glaze application PM 14 3 best performing 5 sources First-fire sanitaryware spray machine glaze application PM 4 3 best performing 5 sources First-fire sanitaryware robot glaze application PM 10 4 best performing 5 sources**No. of**

**Sources in MA** **CT Floor (N)**  **No. Data**

**Points in MA** **CT Floor (n)**  **Av erage of** 

**Top Sources**  **UPL Unit of Measure**  **Data Distribution** 1 3 3.5E-05 3.9E-05 lb/ton Lognormal 1 3 0.020 0.03 lb/ton Normal 1 3 1.1 1.5 ng/dscm @ 7% O2 Lognormal 1 3 0.0070 0.012 ng/dscm @ 7% O2 Normal 1 3 0.010 0.015 ng/dscm @ 7% O2 Normal 1 6 5.0E-05 2.0E-04 lb/ton Normal 1 9 0.071 0.20 lb/ton Normal 1 6 0.065 0.17 ng/dscm @ 7% O2 Normal 1 3 0.053 0.12 ng/dscm @ 7% O2 Normal 1 3 7.4E-06 3.4E-05 lb/ton Lognormal 1 3 0.15 0.61 lb/ton Normal 1 3 6.4E-05 1.2E-04 lb/ton Normal 1 3 0.092 0.095 lb/ton Lognormal 1 3 0.23 0.37 ng/dscm @ 7% O2 Lognormal 1 3 3.3 3.8 lb/ton Lognormal 1 3 2.0 3.2 lb/ton Normal 1 3 1.3 2.2 lb/ton LognormalFloor Tile Floor Tile Floor Tile Floor Tile Roller Kiln Roller Kiln Roller Kiln Press Dryer Hg PM TEQ TEQ lb/ton lb/ton ng/dscm @ 7% O2 ng/dscm @ 7% O2 Runs 36 77 84 PD-203 1 3.35E-05 1.85E-02 1.04E+00 7.55E-03 2 3.61E-05 2.11E-02 1.26E+00 7.57E-03 3 3.39E-05 1.99E-02 1.07E+00 5.89E-03 Average 3.45E-05 1.98E-02 1.12E+00 7.00E-03 Standard Deviation

1.42E-06 1.32E-03 1.18E-01 9.66E-04 1 9.57E-25 3.34E-12 4.72E-05 8.75E-14 2 7.10E-24 2.83E-12 3.29E-04 1.07E-13 3 1.71E-25 9.27E-18 7.18E-06 1.55E-12 Testing Normality

Raw Data Raw Data Raw Data Raw Data Sample Size 3.00 3.00 3.00 3.00 Kurtosis -2.00 -2.00 -2.00 -2.00 SE Kurtosis 2.83 2.83 2.83 2.83 Result Kurtosis normal normal normal normal Skewness 1.62 -0.19 1.60 -1.73 SE Skewness 1.22 1.22 1.22 1.22 Result Skewnessnormal normal normal normal

1.321136685 0.152728268 1.303530926 1.412924941 Lognormal Normal Lognormal Normal 1 2 3 4Floor Tile Wall Tile Wall Tile Wall Tile Wall Tile

Spray Dryer Roller Kiln Roller Kiln Roller Kiln Spray Dryer TEQ Hg PM TEQ TEQ ng/dscm @ 7% O2 lb/ton lb/ton ng/dscm @ 7% O2 ng/dscm @ 7% O2 SD-104 70 70 [n>3] 70 SD-105 9.11E-03 1.14E-06 3.06E-02 5.90E-02 1.03E-02 9.87E-07 2.96E-02 5.95E-02 1.09E-02 1.12E-06 1.07E-02 3.96E-02 1.01E-02 1.08E-06 #DIV/0! 2.36E-02 5.27E-02 8.98E-04 8.43E-08 #DIV/0! 1.12E-02 1.14E-02 9.25E-13 1.01E-29 #DIV/0! 2.35E-09 1.59E-09 1.61E-15 8.82E-29 #DIV/0! 1.26E-09 2.14E-09 3.71E-13 2.71E-30 #DIV/0! 2.79E-08 2.96E-08 Raw Data Raw Data Raw Data Raw Data Raw Data 3.00 3.00 0.00 3.00 3.00 -2.00 -2.00 #DIV/0! -2.00 -2.00 2.83 2.83 #DIV/0! 2.83 2.83 normal normal #DIV/0! normal normal -0.95 -1.66 #DIV/0! -1.72 -1.73 1.22 1.22 0.00 1.22 1.22 normal normal #DIV/0! normal normal 0.778657515 1.358786394 #DIV/0! 1.40154496 1.411216784 Normal Normal #DIV/0! Normal Normal 5 6 7 8 9Tile Tile Sanitaryware Sanitaryware Sanitaryware

Glazing Glazing Tunnel Kiln Tunnel Kiln Tunnel Kiln Hg PM Hg PM TEQ lb/ton lb/ton lb/ton lb/ton ng/dscm @ 7% O2 GL-3, 4, 5 GL-1 TK #2 POC + EE + FE stack TK #6 POC stack TK #10 POC + RCE stacks 2.87E-06 1.52E-01 7.38E-05 9.21E-02 2.87E-01 4.08E-06 2.33E-01 6.53E-05 9.33E-02 2.19E-01 1.52E-05 7.21E-02 5.41E-05 9.15E-02 1.99E-01 7.37E-06 1.52E-01 6.44E-05 9.23E-02 2.35E-01 6.79E-06 8.04E-02 9.92E-06 8.96E-04 4.62E-02 4.12E-22 1.36E-13 7.98E-21 2.39E-15 7.35E-06 1.19E-22 4.24E-05 5.88E-25 9.44E-13 6.63E-08 3.71E-21 4.11E-05 1.14E-20 3.42E-13 1.68E-06 Raw Data Raw Data Raw Data Raw Data Raw Data 3.00 3.00 3.00 3.00 3.00 -2.00 -2.00 -2.00 -2.00 -2.00 2.83 2.83 2.83 2.83 2.83 normal normal normal normal normal 1.67 0.03 -0.39 1.04 1.37 1.22 1.22 1.22 1.22 1.22 normal normal normal normal normal 1.364259977 0.02777046 0.321944145 0.851649774 1.122364916 Lognormal Normal Normal Lognormal Lognormal 10 11 12 13 14Sanitaryware Sanitaryware Sanitaryware

Manual Glaze Application Spray Machine

Glaze Application Robot Glaze

Application PM PM PM lb/ton lb/ton lb/ton SO3/SO4 EO14 (EPN014-

Bowl SM 1) SR1 (EPN 104-1P) Example 18 3.52E+00 2.14E+00 1.68E+00 3.17E+00 1.72E+00 1.17E+00 3.29E+00 2.01E+00 1.10E+00 3.33E+00 1.95E+00 1.32E+00 #DIV/0! 1.75E-01 2.16E-01 3.19E-01 #DIV/0! 1.31E-03 1.18E-03 1.78E-02 #DIV/0! 5.69E-04 3.18E-03 4.38E-04 #DIV/0! 1.61E-06 7.32E-06 2.37E-03 #DIV/0! Raw Data Raw Data Raw Data Raw Data 3.00 3.00 3.00 0.00 -2.00 -2.00 -2.00 #DIV/0! 2.83 2.83 2.83 #DIV/0! normal normal normal #DIV/0! 0.88 -1.02 1.62 #DIV/0! 1.22 1.22 1.22 0.00 normal normal normal #DIV/0! 0.716530195 0.833009191 1.324485629 #DIV/0! Lognormal 15 16 17 18Example 1 Example 2 Example 3 Example 4 Example 5

-1.03E+01 -3.99E+00 3.68E-02 -4.89E+00 -4.70E+00 -1.02E+01 -3.86E+00 2.27E-01 -4.88E+00 -4.58E+00 -1.03E+01 -3.92E+00 6.63E-02 -5.14E+00 -4.52E+00 -1.03E+01 -3.92E+00 1.10E-01 -4.97E+00 -4.60E+00 4.08E-02 6.71E-02 1.02E-01 1.44E-01 9.04E-02 6.61E-07 2.29E-05 2.89E-05 4.42E-05 9.81E-05 4.78E-06 1.77E-05 1.88E-04 5.27E-05 2.49E-07 1.11E-07 3.36E-10 3.66E-06 7.73E-04 3.55E-05 Log Data Log Data Log Data Log Data Log Data 3.00 3.00 3.00 3.00 3.00 -2.00 -2.00 -2.00 -2.00 -2.00 2.83 2.83 2.83 2.83 2.83 normal normal normal normal normal 1.61 -0.29 1.57 -1.73 -1.04 1.22 1.22 1.22 1.22 1.22 normal normal normal normal normal 1.314519853 0.233288022 1.28273836 1.413204771 0.851958742Example 6 Example 7 Example 8 Example 9 Example 10

-1.37E+01 #NUM! -3.49E+00 -2.83E+00 -1.28E+01 -1.38E+01 #NUM! -3.52E+00 -2.82E+00 -1.24E+01 -1.37E+01 #NUM! -4.54E+00 -3.23E+00 -1.11E+01 -1.37E+01 #NUM! -3.85E+00 -2.96E+00 -1.21E+01 7.97E-02 #NUM! 5.97E-01 2.33E-01 8.78E-01 7.76E-06 #NUM! 1.70E-02 2.88E-04 2.04E-01 7.05E-05 #NUM! 1.16E-02 3.69E-04 1.07E-02 2.28E-06 #NUM! 2.25E-01 5.23E-03 9.74E-01 Log Data Log Data Log Data Log Data Log Data 3.00 0.00 3.00 3.00 3.00 -2.00 #NUM! -2.00 -2.00 -2.00 2.83 #DIV/0! 2.83 2.83 2.83 normal #NUM! normal normal normal -1.67 #NUM! -1.73 -1.73 1.43 1.22 0.00 1.22 1.22 1.22 normal #NUM! normal normal normal 1.365733998 #NUM! 1.409280588 1.412183555 1.165199367Example 11 Example 12 Example 13 Example 14 Example 15

-1.89E+00 -9.51E+00 -2.39E+00 -1.25E+00 1.26E+00 -1.46E+00 -9.64E+00 -2.37E+00 -1.52E+00 1.16E+00 -2.63E+00 -9.83E+00 -2.39E+00 -1.62E+00 1.19E+00 -1.99E+00 -9.66E+00 -2.38E+00 -1.46E+00 1.20E+00 5.93E-01 1.57E-01 9.69E-03 1.90E-01 5.22E-02 1.19E-04 4.43E-04 3.14E-11 2.04E-03 1.01E-05 8.13E-02 2.18E-07 1.29E-08 1.17E-05 4.71E-06 1.66E-01 7.72E-04 4.72E-09 5.66E-04 9.37E-09 Log Data Log Data Log Data Log Data Log Data 3.00 3.00 3.00 3.00 3.00 -2.00 -2.00 -2.00 -2.00 -2.00 2.83 2.83 2.83 2.83 2.83 normal normal normal normal normal -0.77 -0.61 1.03 1.25 0.82 1.22 1.22 1.22 1.22 1.22 normal normal normal normal normal 0.627460159 0.496426548 0.844039835 1.021912981 0.667740396Example 16 Example 17 Example 18

7.60E-01 5.21E-01 #NUM! 5.40E-01 1.61E-01 #NUM! 6.96E-01 9.41E-02 #NUM! 6.65E-01 2.59E-01 #NUM! 1.13E-01 2.30E-01 #NUM! 8.11E-05 4.76E-03 #NUM! 2.47E-04 9.19E-05 #NUM! 8.65E-07 7.36E-04 #NUM! Log Data Log Data Log Data 3.00 3.00 0.00 -2.00 -2.00 #NUM! 2.83 2.83 #DIV/0! normal normal #NUM! -1.12 1.57 #NUM! 1.22 1.22 0.00 normal normal #NUM! 0.917542655 1.281129305 #NUM!Raw Data: Floor Tile - Roller Kiln - Hg lb/ton Runs 36 1 3.35E-05 2 3.61E-05 3 3.39E-05 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 3.45E-05 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.62 1.61 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs 36 1 -1.03E+01 2 -1.02E+01 3 -1.03E+01 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate -1.03E+01

0.001666692 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 FT-RK-Hg 12/1/20143.026731076
8.34749E-06

362593.6779
7. Calculate 0.070780028

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 3.4526E-05
b- Calculate 1.19204E-09

c- Calculate 0.001668082

d-calculate 0.000556259

e- Calculate 3.45E-06

f- Calculate UPL 3.85E-05 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 FT-RK-Hg 12/1/2014∆z z

0.101 362593.7 0.07078

-5=f(a) 7221597 1 -4.899 6572083 2 -4.798 5965109 3 -4.697 5398863 4 -4.596 4871571 5 -4.495 4381499 6 -4.394 3926947 7 -4.293 3506256 8 -4.192 3117802 9 -4.091 2760002 10 -3.99 2431307 11 -3.889 2130208 12 -3.788 1855234 13 -3.687 1604950 14 -3.586 1377961 15 -3.485 1172908 16 -3.384 988469.8 17 -3.283 823363.6 18 -3.182 676344 19 -3.081 546203.6 20 -2.98 431772.3 21 -2.879 331918.2 22 -2.778 245546.8 23 -2.677 171601.4 24 -2.576 109063.1 25 -2.475 56950.79 26 -2.374 14320.88 27 -2.273 -19732.3 28 -2.172 -46076.8 29 -2.071 -65542.9 30 -1.97 -78923.2 31 -1.869 -86972.3 32 -1.768 -90407.5 33 -1.667 -89908 34 -1.566 -86115.6 35 -1.465 -79634 36 -1.364 -71029.4 37 -1.263 -60830.4 38 -1.162 -49527.4 39 -1.061 -37573.6

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -25384.2

41 -0.859 -13336.5 42 -0.758 -1770.54 43 -0.657 9011.804 44 -0.556 18746.19 45 -0.455 27206.03 46 -0.354 34202.5 47 -0.253 39584.48 48 -0.152 43238.58 49 -0.051 45089.16 50 0.05 45098.31 51 0.151 43265.83 52 0.252 39629.26 53 0.353 34263.89 54 0.454 27282.73 55 0.555 18836.5 56 0.656 9113.686 57 0.757 -1659.52 58 0.858 -13219.2 59 0.959 -25263.6 60 1.06 -37453.5 61 1.161 -49411.6 62 1.262 -60723.1 63 1.363 -70935.5 64 1.464 -79558.3 65 1.565 -86063.6 66 1.666 -89885.6 67 1.767 -90420.7 68 1.868 -87027.8 69 1.969 -79027.7 70 2.07 -65703.9 71 2.171 -46301.9 72 2.272 -20029.4 73 2.373 13943.29 74 2.474 56483.94 75 2.575 108497.9 76 2.676 170928.2 77 2.777 244755.8 78 2.878 330999.1 79 2.979 430714.5 80 3.08 544995.9 81 3.181 674975.3 82 3.282 821821.9 83 3.383 986743.1 84 3.484 1170984 85 3.585 1375827 86 3.686 1602592 87 3.787 1852638 88 3.888 212736189 3.989 2428194

90 4.09 2756608 91 4.191 3114113 92 4.292 3502256 93 4.393 3922620 94 4.494 4376829 95 4.595 4866541 96 4.696 5393456 97 4.797 5959308 98 4.898 6565871 99 4.999 7214955distribution of Z Normal distribution

1.48672E-06 10.73648974 2.45094E-06 16.1077804 3.9995E-06 23.85746918 6.46025E-06 34.87798606 1.03291E-05 50.31889059 1.63472E-05 71.62544432 2.56093E-05 100.5662095 3.97118E-05 139.2396071 6.09553E-05 190.0464178 9.26132E-05 255.6125344 0.000139285 338.644485 0.000207351 441.7000994 0.000305546 566.8591241 0.000445674 715.2845308 0.000643469 886.6755533 0.000919619 1078.628602 0.001300942 1285.942062 0.001821704 1499.924606 0.002525035 1707.792031 0.003464389 1892.261533 0.004704958 2031.470449 0.006324913 2099.353634 0.008416337 2066.604499 0.011085658 1902.314506 0.014453386 1576.331661 0.018652949 1062.300079 0.023828414 341.2437482 0.030130931 -594.5535287 0.03771375 -1737.730562 0.046725789 -3062.545433 0.057303789 -4522.595769 0.069563239 -6050.075597 0.083588399 -7557.017202 0.099421884 -8938.826343 0.117054396 -10080.20668 0.136415346 -10863.29884 0.157365126 -11177.55792 0.179689839 -10930.59789 0.203099244 -10058.98376 0.227228529 -8537.797812 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -6387.778425 0.275855243 -3678.953708 0.299326439 -529.9691644 0.321498297 2897.279649 0.341807853 6407.593656 0.359712192 9786.341653 0.37471238 12816.10021 0.386376486 15294.51087 0.394360216 17051.5761 0.398423793 17964.59582 0.398443914 17969.14645 0.394419966 17064.90576 0.386474058 15315.68213 0.374844865 12843.64488 0.359875719 9818.391247 0.34199778 6442.04169 0.32170943 2931.95862 0.299553264 -497.1141621 0.276092166 -3649.71155 0.25188591 -6363.552364 0.227469632 -8519.528826 0.203335281 -10047.12068 0.17991684 -10925.11289 0.157579839 -11178.00125 0.136615273 -10868.88333 0.117237788 -10089.91049 0.099587708 -8951.501856 0.083736272 -7571.495186 0.069693339 -6065.255472 0.05741676 -4537.515858 0.046822635 -3076.42995 0.037795734 -1750.013 0.030199481 -604.878573 0.023885038 333.0359363 0.018699163 1056.202315 0.014490659 1572.205774 0.011115369 1899.930118 0.008439746 2065.676485 0.006343145 2099.575251 0.004718997 2032.540229 0.003475077 1893.903092 0.002533081 1709.766853 0.001827693 1502.038506 0.001305351 1288.046452 0.000922829 1080.61787 0.00064578 888.4818841 0.00044732 716.8713341 0.000306705 568.2140508 0.000208159 442.82835490.000139842 339.5629115 9.29928E-05 256.3447138 6.12113E-05 190.6188728 3.98826E-05 139.6790522 2.5722E-05 100.8977243 1.64209E-05 71.87140348 1.03767E-05 50.49847029 6.49066E-06 35.00708314 4.01874E-06 23.94888848 2.46298E-06 16.17157618 1.49417E-06 10.78037585Absolute values

10.73648974 0.542192732 16.1077804 1.62688582 23.85746918 2.409604387 34.87798606 3.522676592 50.31889059 5.08220795 71.62544432 7.234169876 100.5662095 10.15718715 139.2396071 14.06320032 190.0464178 19.19468819 255.6125344 25.81686597 338.644485 34.20309298 441.7000994 44.61171004 566.8591241 57.25277153 715.2845308 72.24373761 886.6755533 89.55423088 1078.628602 108.9414888 1285.942062 129.8801482 1499.924606 151.4923852 1707.792031 172.4869951 1892.261533 191.1184148 2031.470449 205.1785153 2099.353634 212.034717 2066.604499 208.7270544 1902.314506 192.1337651 1576.331661 159.2094977 1062.300079 107.2923079 341.2437482 34.46561857 594.5535287 60.0499064 1737.730562 175.5107867 3062.545433 309.3170888 4522.595769 456.7821726 6050.075597 611.0576353 7557.017202 763.2587374 8938.826343 902.8214606 10080.20668 1018.100875 10863.29884 1097.193183 11177.55792 1128.93335 10930.59789 1103.990387 10058.98376 1015.95736 8537.797812 862.317579 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 6387.778425 645.1656209 3678.953708 371.5743245 529.9691644 53.5268856 2897.279649 292.6252446 6407.593656 647.1669592 9786.341653 988.420507 12816.10021 1294.426122 15294.51087 1544.745598 17051.5761 1722.209186 17964.59582 1814.424178 17969.14645 1814.883791 17064.90576 1723.555482 15315.68213 1546.883895 12843.64488 1297.208133 9818.391247 991.6575159 6442.04169 650.6462107 2931.95862 296.1278206 497.1141621 50.20853037 3649.71155 368.6208666 6363.552364 642.7187888 8519.528826 860.4724115 10047.12068 1014.759189 10925.11289 1103.436402 11178.00125 1128.978126 10868.88333 1097.757216 10089.91049 1019.080959 8951.501856 904.1016875 7571.495186 764.7210138 6065.255472 612.5908026 4537.515858 458.2891016 3076.42995 310.719425 1750.013 176.751313 604.878573 61.09273587 333.0359363 33.63662956 1056.202315 106.6764338 1572.205774 158.7927832 1899.930118 191.8929419 2065.676485 208.633325 2099.575251 212.0571004 2032.540229 205.2865631 1893.903092 191.2842123 1709.766853 172.6864521 1502.038506 151.7058891 1288.046452 130.0926916 1080.61787 109.1424049 888.4818841 89.73667029 716.8713341 72.40400475 568.2140508 57.38961913 442.8283549 44.72566384339.5629115 34.29585406 256.3447138 25.8908161 190.6188728 19.25250616 139.6790522 14.10758427 100.8977243 10.19067016 71.87140348 7.259011752 50.49847029 5.1003455 35.00708314 3.535715397 23.94888848 2.418837736 16.17157618 1.633329195 10.78037585 0.544408981Cumulative normalization
0.542192732 1.28191E-05 2.169078552 5.12837E-05 4.57868294 0.000108254 8.101359531 0.000191541 13.18356748 0.0003117 20.41773736 0.000482738 30.57492451 0.000722885 44.63812483 0.001055382 63.83281303 0.001509204 89.649679 0.002119594 123.852772 0.00292826 168.464482 0.003983018 225.7172536 0.00533665 297.9609912 0.007044714 387.5152221 0.009162051 496.4567108 0.011737763 626.3368591 0.014808528 777.8292443 0.018390274 950.3162394 0.022468397 1141.434654 0.026987024 1346.61317 0.031838074 1558.647887 0.036851227 1767.374941 0.041786176 1959.508706 0.046328809 2118.718204 0.050093011 2226.010512 0.052629731 2260.47613 0.053444604 2320.526037 0.054864368 2496.036823 0.059013982 2805.353912 0.066327189 3262.136085 0.077126924 3873.19372 0.091574204 4636.452458 0.109619987 5539.273918 0.130965461 6557.374793 0.155036495 7654.567976 0.180977515 8783.501326 0.207668969 9887.491713 0.233770695 10903.44907 0.25779105 11765.76665 0.278178888 

## ( ) 2 () () f a f x f b        12410.93227 0.293432586 12782.5066 0.302217745 12836.03348 0.303483285 13128.65873 0.310401845 13775.82569 0.325702862 14764.24619 0.34907216 16058.67232 0.379676373 17603.41791 0.416198907 19325.6271 0.456917225 21140.05128 0.49981579 22954.93507 0.542725221 24678.49055 0.58347537 26225.37445 0.62004846 27522.58258 0.650718447 28514.24009 0.674164279 29164.8863 0.689547555 29461.01413 0.696548927 29511.22266 0.697736011 29879.84352 0.706451342 30522.56231 0.721647189 31383.03472 0.741991402 32397.79391 0.765983428 33501.23031 0.792072056 34630.20844 0.818764569 35727.96565 0.844718924 36747.04661 0.86881313 37651.1483 0.890188873 38415.86932 0.908269228 39028.46012 0.922752758 39486.74922 0.933588121 39797.46864 0.940934483 39974.21996 0.945113427 40035.31269 0.946557847 40068.94932 0.947353121 40175.62576 0.949875279 40334.41854 0.953629629 40526.31148 0.958166568 40734.94481 0.963099301 40947.00191 0.968112983 41152.28847 0.972966588 41343.57268 0.977489135 41516.25913 0.981571973 41667.96502 0.985158767 41798.05772 0.988234558 41907.20012 0.99081502 41996.93679 0.99293667 42069.3408 0.994648524 42126.73041 0.996005391 42171.45608 0.99706284342205.75193 0.997873702 42231.64275 0.998485841 42250.89525 0.998941029 42265.00284 0.999274576 42275.19351 0.999515514 42282.45252 0.99968714 42287.55287 0.999807728 42291.08858 0.999891323 42293.50742 0.999948512 42295.14075 0.999987128 42295.68516 1 2135744.65Raw Data: Floor Tile - Roller Kiln - PM lb/ton Runs 77 1 1.85E-02 2 2.11E-02 3 1.99E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -0.19 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 1.98E-02 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1.98E-02 Mean =

Pooled Variance = 1.76E-06

m= number future runs = 3
Term1 6.67E-01

Term2 1.17E-06

Squared root Term2 1.08E-03 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 2.73E-02 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 FT-RK-PM 12/1/2014Raw Data: Floor Tile - Roller Kiln - TEQ ng/dscm @ 7% O2 Runs 84 1 1.04E+00 2 1.26E+00 3 1.07E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 1.12E+00 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.60 1.57 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs 84 1 3.68E-02 2 2.27E-01 3 6.63E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate 1.10E-01

0.010495869 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 FT-RK-TEQ 12/1/20143.170495265
0.00033398

9495.071416
7. Calculate 0.178539847

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 1.122251385
b- Calculate 1.259448172

c- Calculate 0.010551144

d-calculate 0.003526164

e- Calculate 0.282551

f- Calculate UPL 1.45E+00 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 FT-RK-TEQ 12/1/2014∆z z

0.101 9495.071 0.17854

-5=f(a) 189048.1 1 -4.899 172045.1 2 -4.798 156155.6 3 -4.697 141332.3 4 -4.596 127528.8 5 -4.495 114699.7 6 -4.394 102800.4 7 -4.293 91787.45 8 -4.192 81618.48 9 -4.091 72251.95 10 -3.99 63647.36 11 -3.889 55765.18 12 -3.788 48566.9 13 -3.687 42014.98 14 -3.586 36072.86 15 -3.485 30704.98 16 -3.384 25876.77 17 -3.283 21554.63 18 -3.182 17705.96 19 -3.081 14299.16 20 -2.98 11303.6 21 -2.879 8689.638 22 -2.778 6428.628 23 -2.677 4492.909 24 -2.576 2855.805 25 -2.475 1491.631 26 -2.374 375.6882 27 -2.273 -515.734 28 -2.172 -1205.36 29 -2.071 -1714.92 30 -1.97 -2065.17 31 -1.869 -2275.86 32 -1.768 -2365.76 33 -1.667 -2352.67 34 -1.566 -2253.38 35 -1.465 -2083.69 36 -1.364 -1858.42 37 -1.263 -1591.42 38 -1.162 -1295.52 39 -1.061 -982.588

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -663.486

41 -0.859 -348.099 42 -0.758 -45.3221 43 -0.657 236.9388 44 -0.556 491.7645 45 -0.455 713.2237 46 -0.354 896.3731 47 -0.253 1037.257 48 -0.152 1132.907 49 -0.051 1181.344 50 0.05 1181.574 51 0.151 1133.594 52 0.252 1038.386 53 0.353 897.9205 54 0.454 715.1567 55 0.555 494.0407 56 0.656 239.5066 57 0.757 -42.5239 58 0.858 -345.141 59 0.959 -660.448 60 1.06 -979.56 61 1.161 -1292.6 62 1.262 -1588.72 63 1.363 -1856.05 64 1.464 -2081.78 65 1.565 -2252.07 66 1.666 -2352.11 67 1.767 -2366.1 68 1.868 -2277.25 69 1.969 -2067.8 70 2.07 -1718.98 71 2.171 -1211.03 72 2.272 -523.222 73 2.373 366.1717 74 2.474 1479.865 75 2.575 2841.558 76 2.676 4475.942 77 2.777 6408.692 78 2.878 8666.473 79 2.979 11276.94 80 3.08 14268.73 81 3.181 17671.46 82 3.282 21515.77 83 3.383 25833.25 84 3.484 30656.48 85 3.585 36019.06 86 3.686 41955.54 87 3.787 48501.48 88 3.888 55693.4389 3.989 63568.91

90 4.09 72166.43 91 4.191 81525.51 92 4.292 91686.64 93 4.393 102691.3 94 4.494 114582 95 4.595 127402.1 96 4.696 141196.1 97 4.797 156009.4 98 4.898 171888.5 99 4.999 188880.7distribution of Z Normal distribution

1.48672E-06 0.281061573 2.45094E-06 0.421672107 3.9995E-06 0.624544769 6.46025E-06 0.913041785 1.03291E-05 1.317256601 1.63472E-05 1.875023676 2.56093E-05 2.632641018 3.97118E-05 3.645041944 6.09553E-05 4.97507532 9.26132E-05 6.691483567 0.000139285 8.865120769 0.000207351 11.56294953 0.000305546 14.8394188 0.000445674 18.72498041 0.000643469 23.2117715 0.000919619 28.23688558 0.001300942 33.66417483 0.001821704 39.26614469 0.002525035 44.70816606 0.003464389 49.53785638 0.004704958 53.18295458 0.006324913 54.96120246 0.008416337 54.10550473 0.011085658 49.80684942 0.014453386 41.27604955 0.018652949 27.82331266 0.023828414 8.952055043 0.030130931 -15.5395327 0.03771375 -45.45855476 0.046725789 -80.13094333 0.057303789 -118.3417902 0.069563239 -158.3159057 0.083588399 -197.750342 0.099421884 -233.906954 0.117054396 -263.7675041 0.136415346 -284.2467408 0.157365126 -292.4509854 0.179689839 -285.9620217 0.203099244 -263.1196187 0.227228529 -223.2719498 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -166.9624628 0.275855243 -96.0249832 0.299326439 -13.5660893 0.321498297 76.17542357 0.341807853 168.0889568 0.359712192 256.5552684 0.37471238 335.8821059 0.386376486 400.7717015 0.394360216 446.7735695 0.398423793 470.6755305 0.398443914 470.7911266 0.394419966 447.1121017 0.386474058 401.3091544 0.374844865 336.5808792 0.359875719 257.3675337 0.34199778 168.9608329 0.32170943 77.05152667 0.299553264 -12.73818613 0.276092166 -95.29081438 0.25188591 -166.35761 0.227469632 -222.8200906 0.203335281 -262.8317819 0.17991684 -285.8370103 0.157579839 -292.4768089 0.136615273 -284.4028098 0.117237788 -264.0272882 0.099587708 -234.2407938 0.083736272 -198.1281292 0.069693339 -158.7094005 0.05741676 -118.7264174 0.046822635 -80.48698388 0.037795734 -45.77172754 0.030199481 -15.80102209 0.023885038 8.746024642 0.018699163 27.67222808 0.014490659 41.17605202 0.011115369 49.75174434 0.008439746 54.08773332 0.006343145 54.97269775 0.004718997 53.21583324 0.003475077 49.58492546 0.002533081 44.76324671 0.001827693 39.32423185 0.001305351 33.72146266 0.000922829 28.29069302 0.00064578 23.26040237 0.00044732 18.76754876 0.000306705 14.87566457 0.000208159 11.593063010.000139842 8.889587867 9.29928E-05 6.710958295 6.12113E-05 4.990281253 3.98826E-05 3.65670131 2.5722E-05 2.641427952 1.64209E-05 1.881537182 1.03767E-05 1.322008539 6.49066E-06 0.916455513 4.01874E-06 0.62696068 2.46298E-06 0.423357077 1.49417E-06 0.282220104Absolute values

0.281061573 0.014193609 0.421672107 0.042588883 0.624544769 0.063079022 0.913041785 0.09221722 1.317256601 0.133042917 1.875023676 0.189377391 2.632641018 0.265896743 3.645041944 0.368149236 4.97507532 0.502482607 6.691483567 0.67583984 8.865120769 0.895377198 11.56294953 1.167857903 14.8394188 1.498781299 18.72498041 1.891223022 23.2117715 2.344388922 28.23688558 2.851925444 33.66417483 3.400081658 39.26614469 3.965880614 44.70816606 4.515524773 49.53785638 5.003323494 53.18295458 5.371478413 54.96120246 5.551081449 54.10550473 5.464655978 49.80684942 5.030491792 41.27604955 4.168881004 27.82331266 2.810154579 8.952055043 0.904157559 15.5395327 1.569492803 45.45855476 4.591314031 80.13094333 8.093225276 118.3417902 11.95252081 158.3159057 15.98990648 197.750342 19.97278454 233.906954 23.62460235 263.7675041 26.64051791 284.2467408 28.70892082 292.4509854 29.53754952 285.9620217 28.88216419 263.1196187 26.57508149 223.2719498 22.55046693 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 166.9624628 16.86320875 96.0249832 9.698523303 13.5660893 1.370175019 76.17542357 7.69371778 168.0889568 16.97698463 256.5552684 25.91208211 335.8821059 33.9240927 400.7717015 40.47794185 446.7735695 45.12413052 470.6755305 47.53822858 470.7911266 47.54990378 447.1121017 45.15832227 401.3091544 40.53222459 336.5808792 33.99466879 257.3675337 25.9941209 168.9608329 17.06504412 77.05152667 7.782204194 12.73818613 1.286556799 95.29081438 9.624372253 166.35761 16.80211861 222.8200906 22.50482915 262.8317819 26.54600997 285.8370103 28.86953804 292.4768089 29.5401577 284.4028098 28.72468379 264.0272882 26.66675611 234.2407938 23.65832018 198.1281292 20.01094105 158.7094005 16.02964946 118.7264174 11.99136816 80.48698388 8.129185372 45.77172754 4.622944482 15.80102209 1.595903231 8.746024642 0.883348489 27.67222808 2.794895037 41.17605202 4.158781254 49.75174434 5.024926179 54.08773332 5.462861065 54.97269775 5.552242473 53.21583324 5.374799157 49.58492546 5.008077472 44.76324671 4.521087918 39.32423185 3.971747417 33.72146266 3.405867729 28.29069302 2.857359995 23.26040237 2.349300639 18.76754876 1.895522425 14.87566457 1.502442121 11.59306301 1.1708993648.889587867 0.897848375 6.710958295 0.677806788 4.990281253 0.504018407 3.65670131 0.369326832 2.641427952 0.266784223 1.881537182 0.190035255 1.322008539 0.133522862 0.916455513 0.092562007 0.62696068 0.063323029 0.423357077 0.042759065 0.282220104 0.014252115Cumulative normalization
0.014193609 1.2818E-05 0.056782492 5.12794E-05 0.119861514 0.000108245 0.212078734 0.000191525 0.345121651 0.000311674 0.534499042 0.000482698 0.800395785 0.000722825 1.168545021 0.001055295 1.671027629 0.001509079 2.346867469 0.00211942 3.242244667 0.002928021 4.410102569 0.003982696 5.908883868 0.005336222 7.80010689 0.007044156 10.14449581 0.009161338 12.99642126 0.011736868 16.39650291 0.014807429 20.36238353 0.018388955 24.8779083 0.022466856 29.8812318 0.02698528 35.25271021 0.031836179 40.80379166 0.036849275 46.26844763 0.041784322 51.29893943 0.046327282 55.46782043 0.050092134 58.27797501 0.052629941 59.18213257 0.053446472 60.75162537 0.054863857 65.3429394 0.059010201 73.43616468 0.066319068 85.38868549 0.077113206 101.378592 0.091553444 121.3513765 0.109590558 144.9759789 0.130925572 171.6164968 0.154984213 200.3254176 0.180910797 229.8629671 0.207585703 258.7451313 0.23366874 285.3202128 0.257668287 307.8706797 0.278033266 

## ( ) 2 () () f a f x f b        324.7338885 0.29326217 334.4324118 0.302020757 335.8025868 0.303258141 343.4963046 0.310206218 360.4732892 0.325537872 386.3853713 0.348938674 420.309464 0.379574999 460.7874059 0.416130004 505.9115364 0.456880911 553.449765 0.499811953 600.9996688 0.542753538 646.157991 0.583535323 686.6902156 0.62013935 720.6848844 0.650839411 746.6790053 0.674314301 763.7440494 0.68972548 771.5262536 0.696753468 772.8128104 0.697915338 782.4371827 0.70660696 799.2393013 0.721780695 821.7441304 0.742104459 848.2901404 0.766077751 877.1596785 0.792149386 906.6998362 0.818826647 935.4245199 0.844767467 962.0912761 0.868849803 985.7495962 0.890215267 1005.760537 0.90828684 1021.790187 0.922762969 1033.781555 0.933592189 1041.91074 0.940933531 1046.533685 0.945108441 1048.129588 0.946549676 1049.012936 0.947347415 1051.807832 0.949871442 1055.966613 0.953627173 1060.991539 0.958165106 1066.4544 0.963098532 1072.006642 0.968112676 1077.381442 0.972966575 1082.389519 0.977489292 1086.910607 0.981572217 1090.882354 0.985159041 1094.288222 0.988234828 1097.145582 0.990815265 1099.494883 0.992936883 1101.390405 0.9946487 1102.892847 0.996005532 1104.063747 0.9970629531104.961595 0.997873786 1105.639402 0.998485903 1106.14342 0.998941074 1106.512747 0.999274608 1106.779531 0.999515536 1106.969567 0.999687154 1107.103089 0.999807737 1107.195651 0.999891328 1107.258974 0.999948514 1107.301734 0.999987129 1107.315986 1 55914.28786Raw Data: Floor Tile - Press Dryer - TEQ ng/dscm @ 7% O2 Runs PD-203 1 7.55E-03 2 7.57E-03 3 5.89E-03 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -1.73 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 7.00E-03 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

7.00E-03 Mean =

Pooled Variance = 9.33E-07

m= number future runs = 3
Term1 6.67E-01

Term2 6.22E-07

Squared root Term2 7.89E-04 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 1.25E-02 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 FT-PD-TEQ 12/1/2014Raw Data: Floor Tile - Spray Dryer - TEQ ng/dscm @ 7% O2 Runs SD-104 1 9.11E-03 2 1.03E-02 3 1.09E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -0.95 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 1.01E-02 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1.01E-02 Mean =

Pooled Variance = 8.06E-07

m= number future runs = 3
Term1 6.67E-01

Term2 5.37E-07

Squared root Term2 7.33E-04 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 1.52E-02 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 FT-SD-TEQ 12/1/2014Raw Data: Wall Tile - Roller Kiln - Hg lb/ton Runs 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 1 1.03E-04 2 4.77E-05 3 1.49E-04 4 1.14E-06 5 9.87E-07 6 1.12E-06 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 6.00 Kurtosis -0.92 SE Kurtosis 2.06 Result Kurtosis normal Skewness 0.89 SE Skewness 0.85 Result Raw Data Result Skewness normal normal
ni = number test runs = 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 6

5

This step is for QC only:
means 5.05E-05 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

5.05E-05 Mean =

Pooled Variance = 3.95E-09

m= number future runs = 3
Term1 5.00E-01

Term2 1.98E-09

Squared root Term2 4.44E-05 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 3.364929999
UPL POOLED VARIANCE = 2.00E-04 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 WT-RK-Hg 12/1/2014Raw Data: Wall Tile - Roller Kiln - PM lb/ton Runs 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 1 1.93E-01 2 1.21E-01 3 1.59E-01 4 2.29E-02 5 2.35E-02 6 5.01E-02 7 2.45E-02 8 1.64E-02 9 2.82E-02 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 9.00 Kurtosis -0.64 SE Kurtosis 1.56 Result Kurtosis normal Skewness 1.05 SE Skewness 0.72 Result Raw Data Result Skewness normal normal
ni = number test runs = 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 9

8

This step is for QC only:
means 7.10E-02 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

7.10E-02 Mean =

Pooled Variance = 4.65E-03

m= number future runs = 3
Term1 4.44E-01

Term2 2.07E-03

Squared root Term2 4.55E-02 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 2.896459448
UPL POOLED VARIANCE = 0.2027 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 WT-RK-PM 12/1/2014Raw Data: Wall Tile - Roller Kiln - TEQ ng/dscm @ 7% O2 Runs 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 1 1.19E-01 2 9.98E-02 3 9.89E-02 4 3.06E-02 5 2.96E-02 6 1.07E-02 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 6.00 Kurtosis -2.73 SE Kurtosis 2.06 Result Kurtosis normal Skewness 0.00 SE Skewness 0.85 Result Raw Data Result Skewness normal normal
ni = number test runs = 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 6

5

This step is for QC only:
means 6.47E-02 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

6.47E-02 Mean =

Pooled Variance = 2.13E-03

m= number future runs = 3
Term1 5.00E-01

Term2 1.06E-03

Squared root Term2 3.26E-02 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 3.364929999
UPL POOLED VARIANCE = 1.74E-01 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 WT-RK-TEQ 12/1/2014Raw Data: Wall Tile - Spray Dryer - TEQ ng/dscm @ 7% O2 Runs SD-105 1 5.90E-02 2 5.95E-02 3 3.96E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -1.73 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 5.27E-02 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

5.27E-02 Mean =

Pooled Variance = 1.29E-04

m= number future runs = 3
Term1 6.67E-01

Term2 8.60E-05

Squared root Term2 9.27E-03 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 1.17E-01 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 WT-SD-TEQ 12/1/2014Raw Data: Tile - Glazing - Hg lb/ton Runs GL-3, 4, 5 1 2.87E-06 2 4.08E-06 3 1.52E-05 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 7.37E-06 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.67 1.43 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs GL-3, 4, 5 1 -1.28E+01 2 -1.24E+01 3 -1.11E+01 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate -1.21E+01

0.770857237 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 T-Glaze-Hg 12/1/201453.05165528
4.048072476

15.10541143
7. Calculate 2.589604208

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 8.26398E-06
b- Calculate 6.82934E-11

c- Calculate 1.16161848

d-calculate 0.405507632

e- Calculate 2.21E-05

f- Calculate UPL 3.39E-05 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 T-Glaze-Hg 12/1/2014∆z z

0.101 15.10541 2.589604

-5=f(a) 194.6234 1 -4.899 176.0118 2 -4.798 158.691 3 -4.697 142.6032 4 -4.596 127.6919 5 -4.495 113.9017 6 -4.394 101.1787 7 -4.293 89.47007 8 -4.192 78.72433 9 -4.091 68.89123 10 -3.99 59.92178 11 -3.889 51.76825 12 -3.788 44.38419 13 -3.687 37.72437 14 -3.586 31.74486 15 -3.485 26.40296 16 -3.384 21.65726 17 -3.283 17.46758 18 -3.182 13.79501 19 -3.081 10.60191 20 -2.98 7.851881 21 -2.879 5.509805 22 -2.778 3.541808 23 -2.677 1.91528 24 -2.576 0.598872 25 -2.475 -0.43751 26 -2.374 -1.22269 27 -2.273 -1.78424 28 -2.172 -2.14847 29 -2.071 -2.34044 30 -1.97 -2.38394 31 -1.869 -2.30149 32 -1.768 -2.11438 33 -1.667 -1.84261 34 -1.566 -1.50493 35 -1.465 -1.11885 36 -1.364 -0.70059 37 -1.263 -0.26512 38 -1.162 0.173834 39 -1.061 0.603823

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 1.013651

41 -0.859 1.393383 42 -0.758 1.734344 43 -0.657 2.029119 44 -0.556 2.271551 45 -0.455 2.456743 46 -0.354 2.58106 47 -0.253 2.642125 48 -0.152 2.638819 49 -0.051 2.571286 50 0.05 2.440928 51 0.151 2.250406 52 0.252 2.003642 53 0.353 1.705817 54 0.454 1.363373 55 0.555 0.984009 56 0.656 0.576687 57 0.757 0.151625 58 0.858 -0.2797 59 0.959 -0.70454 60 1.06 -1.1089 61 1.161 -1.47752 62 1.262 -1.79389 63 1.363 -2.04022 64 1.464 -2.19748 65 1.565 -2.24537 66 1.666 -2.16233 67 1.767 -1.92555 68 1.868 -1.51094 69 1.969 -0.89318 70 2.07 -0.04567 71 2.171 1.059452 72 2.272 2.451299 73 2.373 4.160245 74 2.474 6.217926 75 2.575 8.657235 76 2.676 11.51233 77 2.777 14.81862 78 2.878 18.61278 79 2.979 22.93274 80 3.08 27.8177 81 3.181 33.30811 82 3.282 39.44568 83 3.383 46.27338 84 3.484 53.83545 85 3.585 62.17738 86 3.686 71.34591 87 3.787 81.38907 88 3.888 92.3561189 3.989 104.2976

90 4.09 117.2652 91 4.191 131.3122 92 4.292 146.4927 93 4.393 162.8623 94 4.494 180.4779 95 4.595 199.3976 96 4.696 219.6806 97 4.797 241.3877 98 4.898 264.5806 99 4.999 289.3226distribution of Z Normal distribution

1.48672E-06 0.00028935 2.45094E-06 0.000431394 3.9995E-06 0.000634685 6.46025E-06 0.000921252 1.03291E-05 0.00131894 1.63472E-05 0.001861979 2.56093E-05 0.002591111 3.97118E-05 0.003553015 6.09553E-05 0.004798662 9.26132E-05 0.006380237 0.000139285 0.008346204 0.000207351 0.010734183 0.000305546 0.013561406 0.000445674 0.016812767 0.000643469 0.020426835 0.000919619 0.024280667 0.001300942 0.028174839 0.001821704 0.031820749 0.002525035 0.03483287 0.003464389 0.036729123 0.004704958 0.036942767 0.006324913 0.034849035 0.008416337 0.029809048 0.011085658 0.021232139 0.014453386 0.008655724 0.018652949 -0.008160799 0.023828414 -0.029134698 0.030130931 -0.053760791 0.03771375 -0.081027031 0.046725789 -0.109359108 0.057303789 -0.136608819 0.069563239 -0.160099436 0.083588399 -0.17673764 0.099421884 -0.183195608 0.117054396 -0.17615906 0.136415346 -0.152627999 0.157365126 -0.110247691 0.179689839 -0.047639348 0.203099244 0.035305615 0.227228529 0.137205758 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 0.255079465 0.275855243 0.384372016 0.299326439 0.519135114 0.321498297 0.652358269 0.341807853 0.776433863 0.359712192 0.883720548 0.37471238 0.967155268 0.386376486 1.020854837 0.394360216 1.040645245 0.398423793 1.024461502 0.398443914 0.972572724 0.394419966 0.887604919 0.386474058 0.774355573 0.374844865 0.639416814 0.359875719 0.490644759 0.34199778 0.336528948 0.32170943 0.185525529 0.299553264 0.045419827 0.276092166 -0.077221715 0.25188591 -0.17746266 0.227469632 -0.252240409 0.203335281 -0.300431991 0.17991684 -0.32275046 0.157579839 -0.321497362 0.136615273 -0.300209101 0.117237788 -0.263241944 0.099587708 -0.215341467 0.083736272 -0.161238177 0.069693339 -0.105302766 0.05741676 -0.051283741 0.046822635 -0.002138419 0.037795734 0.040042762 0.030199481 0.074027951 0.023885038 0.099367614 0.018699163 0.116270005 0.014490659 0.125449043 0.011115369 0.127963767 0.008439746 0.125065364 0.006343145 0.118063543 0.004718997 0.108219524 0.003475077 0.096668657 0.002533081 0.084372127 0.001827693 0.072094608 0.001305351 0.060403024 0.000922829 0.049680921 0.00064578 0.040152934 0.00044732 0.031914448 0.000306705 0.024962463 0.000208159 0.0192247140.000139842 0.014585156 9.29928E-05 0.010904823 6.12113E-05 0.008037787 3.98826E-05 0.005842508 2.5722E-05 0.004189148 1.64209E-05 0.002963607 1.03767E-05 0.002069082 6.49066E-06 0.001425872 4.01874E-06 0.000970074 2.46298E-06 0.000651656 1.49417E-06 0.000432297Absolute values

0.00028935 1.46122E-05 0.000431394 4.35708E-05 0.000634685 6.41032E-05 0.000921252 9.30464E-05 0.00131894 0.000133213 0.001861979 0.00018806 0.002591111 0.000261702 0.003553015 0.000358854 0.004798662 0.000484665 0.006380237 0.000644404 0.008346204 0.000842967 0.010734183 0.001084153 0.013561406 0.001369702 0.016812767 0.001698089 0.020426835 0.00206311 0.024280667 0.002452347 0.028174839 0.002845659 0.031820749 0.003213896 0.03483287 0.00351812 0.036729123 0.003709641 0.036942767 0.003731219 0.034849035 0.003519753 0.029809048 0.003010714 0.021232139 0.002144446 0.008655724 0.000874228 0.008160799 0.000824241 0.029134698 0.002942604 0.053760791 0.00542984 0.081027031 0.00818373 0.109359108 0.01104527 0.136608819 0.013797491 0.160099436 0.016170043 0.17673764 0.017850502 0.183195608 0.018502756 0.17615906 0.017792065 0.152627999 0.015415428 0.110247691 0.011135017 0.047639348 0.004811574 0.035305615 0.003565867 0.137205758 0.013857782 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 0.255079465 0.025763026 0.384372016 0.038821574 0.519135114 0.052432647 0.652358269 0.065888185 0.776433863 0.07841982 0.883720548 0.089255775 0.967155268 0.097682682 1.020854837 0.103106339 1.040645245 0.10510517 1.024461502 0.103470612 0.972572724 0.098229845 0.887604919 0.089648097 0.774355573 0.078209913 0.639416814 0.064581098 0.490644759 0.049555121 0.336528948 0.033989424 0.185525529 0.018738078 0.045419827 0.004587403 0.077221715 0.007799393 0.17746266 0.017923729 0.252240409 0.025476281 0.300431991 0.030343631 0.32275046 0.032597796 0.321497362 0.032471234 0.300209101 0.030321119 0.263241944 0.026587436 0.215341467 0.021749488 0.161238177 0.016285056 0.105302766 0.010635579 0.051283741 0.005179658 0.002138419 0.00021598 0.040042762 0.004044319 0.074027951 0.007476823 0.099367614 0.010036129 0.116270005 0.01174327 0.125449043 0.012670353 0.127963767 0.012924341 0.125065364 0.012631602 0.118063543 0.011924418 0.108219524 0.010930172 0.096668657 0.009763534 0.084372127 0.008521585 0.072094608 0.007281555 0.060403024 0.006100705 0.049680921 0.005017773 0.040152934 0.004055446 0.031914448 0.003223359 0.024962463 0.002521209 0.019224714 0.0019416960.014585156 0.001473101 0.010904823 0.001101387 0.008037787 0.000811816 0.005842508 0.000590093 0.004189148 0.000423104 0.002963607 0.000299324 0.002069082 0.000208977 0.001425872 0.000144013 0.000970074 9.79774E-05 0.000651656 6.58172E-05 0.000432297 2.1831E-05Cumulative normalization
1.46122E-05 8.10525E-06 5.8183E-05 3.22736E-05 0.000122286 6.78311E-05 0.000215333 0.000119443 0.000348546 0.000193335 0.000536605 0.00029765 0.000798308 0.000442814 0.001157162 0.000641868 0.001641827 0.000910707 0.002286231 0.001268152 0.003129198 0.001735738 0.00421335 0.002337108 0.005583052 0.003096869 0.007281142 0.004038784 0.009344252 0.005183173 0.011796599 0.006543468 0.014642258 0.008121929 0.017856154 0.009904648 0.021374273 0.011856118 0.025083915 0.013913823 0.028815134 0.015983497 0.032334887 0.017935872 0.035345601 0.019605888 0.037490047 0.020795393 0.038364275 0.021280319 0.039188516 0.021737518 0.04213112 0.023369755 0.04756096 0.026381638 0.05574469 0.03092108 0.06678996 0.037047792 0.080587451 0.044701137 0.096757494 0.053670515 0.114607996 0.063572028 0.133110752 0.073835341 0.150902817 0.08370444 0.166318245 0.09225524 0.177453262 0.098431734 0.182264836 0.101100671 0.185830703 0.103078625 0.199688484 0.110765413 

## ( ) 2 () () f a f x f b        0.22545151 0.125055932 0.264273084 0.146589911 0.316705731 0.17567383 0.382593916 0.212221416 0.461013736 0.255720187 0.550269511 0.305229566 0.647952193 0.359413274 0.751058532 0.416605436 0.856163702 0.474906332 0.959634314 0.532300553 1.057864159 0.586787767 1.147512255 0.636514763 1.225722168 0.679897101 1.290303267 0.715719657 1.339858387 0.743207438 1.373847811 0.762061067 1.392585889 0.772454911 1.397173292 0.774999502 1.404972685 0.779325756 1.422896414 0.789267887 1.448372695 0.803399352 1.478716326 0.820230692 1.511314123 0.838312398 1.543785356 0.8563239 1.574106475 0.873142753 1.600693912 0.887890566 1.6224434 0.899954812 1.638728456 0.908987987 1.649364035 0.914887447 1.654543693 0.917760557 1.654759673 0.917880359 1.658803992 0.920123707 1.666280815 0.924271034 1.676316944 0.929837984 1.688060215 0.936351871 1.700730568 0.943380003 1.713654909 0.950549018 1.726286511 0.957555655 1.738210928 0.964170022 1.7491411 0.970232891 1.758904635 0.975648636 1.76742622 0.980375483 1.774707775 0.984414496 1.78080848 0.987798503 1.785826253 0.990581816 1.7898817 0.992831336 1.793105059 0.994619305 1.795626268 0.996017797 1.797567964 0.9970948381.799041065 0.997911954 1.800142452 0.998522883 1.800954268 0.998973191 1.801544361 0.99930051 1.801967465 0.999535202 1.80226679 0.999701235 1.802475767 0.999817152 1.80261978 0.999897035 1.802717757 0.999951382 1.802783575 0.999987891 1.802805406 1 89.06411024Raw Data: Tile - Glazing - PM lb/ton Runs GL-1 1 1.52E-01 2 2.33E-01 3 7.21E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness 0.03 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 1.52E-01 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1.52E-01 Mean =

Pooled Variance = 6.46E-03

m= number future runs = 3
Term1 6.67E-01

Term2 4.31E-03

Squared root Term2 6.56E-02 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 6.09E-01 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 T-Glaze-PM 12/1/2014Raw Data: Sanitaryware - Tunnel Kiln - Hg lb/ton Runs TK #2 POC + EE + FE stack 1 7.38E-05 2 6.53E-05 3 5.41E-05 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -0.39 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 6.44E-05 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

6.44E-05 Mean =

Pooled Variance = 9.84E-11

m= number future runs = 3
Term1 6.67E-01

Term2 6.56E-11

Squared root Term2 8.10E-06 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 1.21E-04 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 S-TK-Hg 12/1/2014Raw Data: Sanitaryware - Tunnel Kiln - PM lb/ton Runs TK #6 POC stack 1 9.21E-02 2 9.33E-02 3 9.15E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 9.23E-02 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.04 1.03 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs TK #6 POC stack 1 -2.39E+00 2 -2.37E+00 3 -2.39E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate -2.38E+00

9.39312E-05 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 S-TK-PM 12/1/20143.001503102
2.64717E-08

113385346.5
7. Calculate 0.01678763

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 0.092280273
b- Calculate 0.008515649

c- Calculate 9.39356E-05

d-calculate 3.13126E-05

e- Calculate 0.002191

f- Calculate UPL 9.48E-02 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 S-TK-PM 12/1/2014∆z z

0.101 1.13E+08 0.016788

-5=f(a) 2.26E+09 1 -4.899 2.06E+09 2 -4.798 1.87E+09 3 -4.697 1.69E+09 4 -4.596 1.52E+09 5 -4.495 1.37E+09 6 -4.394 1.23E+09 7 -4.293 1.1E+09 8 -4.192 9.75E+08 9 -4.091 8.63E+08 10 -3.99 7.6E+08 11 -3.889 6.66E+08 12 -3.788 5.8E+08 13 -3.687 5.02E+08 14 -3.586 4.31E+08 15 -3.485 3.67E+08 16 -3.384 3.09E+08 17 -3.283 2.57E+08 18 -3.182 2.11E+08 19 -3.081 1.71E+08 20 -2.98 1.35E+08 21 -2.879 1.04E+08 22 -2.778 76784406 23 -2.677 53661019 24 -2.576 34104740 25 -2.475 17808736 26 -2.374 4477977 27 -2.273 -6170770 28 -2.172 -1.4E+07 29 -2.071 -2E+07 30 -1.97 -2.5E+07 31 -1.869 -2.7E+07 32 -1.768 -2.8E+07 33 -1.667 -2.8E+07 34 -1.566 -2.7E+07 35 -1.465 -2.5E+07 36 -1.364 -2.2E+07 37 -1.263 -1.9E+07 38 -1.162 -1.5E+07 39 -1.061 -1.2E+07

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -7938170

41 -0.859 -4170773 42 -0.758 -553982 43 -0.657 2817754 44 -0.556 5861783 45 -0.455 8507253 46 -0.354 10695112 47 -0.253 12378105 48 -0.152 13520777 49 -0.051 14099472 50 0.05 14102333 51 0.151 13529300 52 0.252 12392116 53 0.353 10714318 54 0.454 8531246 55 0.555 5890036 56 0.656 2849625 57 0.757 -519251 58 0.858 -4134060 59 0.959 -7900467 60 1.06 -1.2E+07 61 1.161 -1.5E+07 62 1.262 -1.9E+07 63 1.363 -2.2E+07 64 1.464 -2.5E+07 65 1.565 -2.7E+07 66 1.666 -2.8E+07 67 1.767 -2.8E+07 68 1.868 -2.7E+07 69 1.969 -2.5E+07 70 2.07 -2.1E+07 71 2.171 -1.4E+07 72 2.272 -6263713 73 2.373 4359856 74 2.474 17662691 75 2.575 33927909 76 2.676 53450425 77 2.777 76536951 78 2.878 1.04E+08 79 2.979 1.35E+08 80 3.08 1.7E+08 81 3.181 2.11E+08 82 3.282 2.57E+08 83 3.383 3.09E+08 84 3.484 3.66E+08 85 3.585 4.3E+08 86 3.686 5.01E+08 87 3.787 5.79E+08 88 3.888 6.65E+0889 3.989 7.59E+08

90 4.09 8.62E+08 91 4.191 9.74E+08 92 4.292 1.1E+09 93 4.393 1.23E+09 94 4.494 1.37E+09 95 4.595 1.52E+09 96 4.696 1.69E+09 97 4.797 1.86E+09 98 4.898 2.05E+09 99 4.999 2.26E+09distribution of Z Normal distribution

1.48672E-06 3357.396374 2.45094E-06 5037.046963 3.9995E-06 7460.443865 6.46025E-06 10906.65787 1.03291E-05 15735.16646 1.63472E-05 22397.91572 2.56093E-05 31447.95068 3.97118E-05 43541.46609 6.09553E-05 59429.20696 9.26132E-05 79932.31282 0.000139285 105897.1381 0.000207351 138123.5375 0.000305546 177261.8642 0.000445674 223675.7866 0.000643469 277271.2481 0.000919619 337296.6189 0.001300942 402125.2997 0.001821704 469039.4245 0.002525035 534041.2451 0.003464389 591726.2577 0.004704958 635257.7907 0.006324913 656485.0151 0.008416337 646243.4679 0.011085658 594867.7368 0.014453386 492928.983 0.018652949 332185.4401 0.023828414 106703.09 0.030130931 -185931.0438 0.03771375 -543415.1043 0.046725789 -957699.4152 0.057303789 -1414273.586 0.069563239 -1891934.123 0.083588399 -2363172.761 0.099421884 -2795281.96 0.117054396 -3152207.519 0.136415346 -3397093.723 0.157365126 -3495372.149 0.179689839 -3418152.773 0.203099244 -3145598.806 0.227228529 -2669918.126 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -1997595.656 0.275855243 -1150529.645 0.299326439 -165821.4223 0.321498297 905903.0098 0.341807853 2003603.336 0.359712192 3060162.631 0.37471238 4007590.797 0.386376486 4782608.658 0.394360216 5332056.558 0.398423793 5617565.146 0.398443914 5618988.607 0.394419966 5336226.156 0.386474058 4789231.18 0.374844865 4016207.027 0.359875719 3070188.142 0.34199778 2014379.253 0.32170943 916751.3666 0.299553264 -155543.3833 0.276092166 -1141381.483 0.25188591 -1990016.323 0.227469632 -2664201.993 0.203335281 -3141886.317 0.17991684 -3416435.281 0.157579839 -3495509.041 0.136615273 -3398838.844 0.117237788 -3155241.299 0.099587708 -2799245.486 0.083736272 -2367700.338 0.069693339 -1896681.517 0.05741676 -1418939.998 0.046822635 -962042.1766 0.037795734 -547256.9948 0.030199481 -189160.8925 0.023885038 104135.3169 0.018699163 330277.5365 0.014490659 491637.7715 0.011115369 594121.1961 0.008439746 645952.4486 0.006343145 656553.6007 0.004718997 635591.7078 0.003475077 592239.073 0.002533081 534658.3646 0.001827693 469700.1149 0.001305351 402783.0852 0.000922829 337918.4636 0.00064578 277835.9353 0.00044732 224171.8651 0.000306705 177685.4645 0.000208159 138476.28070.000139842 106184.2851 9.29928E-05 80161.23333 6.12113E-05 59608.1912 3.98826E-05 43678.865 2.5722E-05 31551.60476 1.64209E-05 22474.81999 1.03767E-05 15791.31627 6.49066E-06 10947.0234 4.01874E-06 7489.028652 2.46298E-06 5056.994608 1.49417E-06 3371.118743Absolute values

3357.396374 169.5485169 5037.046963 508.7417432 7460.443865 753.5048304 10906.65787 1101.572445 15735.16646 1589.251813 22397.91572 2262.189488 31447.95068 3176.243019 43541.46609 4397.688075 59429.20696 6002.349903 79932.31282 8073.163595 105897.1381 10695.61095 138123.5375 13950.47729 177261.8642 17903.44828 223675.7866 22591.25445 277271.2481 28004.39606 337296.6189 34066.95851 402125.2997 40614.65527 469039.4245 47372.98187 534041.2451 53938.16576 591726.2577 59764.35203 635257.7907 64161.03686 656485.0151 66304.98652 646243.4679 65270.59026 594867.7368 60081.64142 492928.983 49785.82728 332185.4401 33550.72945 106703.09 10777.01209 185931.0438 18779.03542 543415.1043 54884.92553 957699.4152 96727.64093 1414273.586 142841.6322 1891934.123 191085.3464 2363172.761 238680.4489 2795281.96 282323.478 3152207.519 318372.9594 3397093.723 343106.466 3495372.149 353032.587 3418152.773 345233.4301 3145598.806 317705.4795 2669918.126 269661.7307 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 1997595.656 201757.1613 1150529.645 116203.4942 165821.4223 16747.96366 905903.0098 91496.20399 2003603.336 202363.9369 3060162.631 309076.4257 4007590.797 404766.6705 4782608.658 483043.4744 5332056.558 538537.7124 5617565.146 567374.0798 5618988.607 567517.8493 5336226.156 538958.8417 4789231.18 483712.3492 4016207.027 405636.9097 3070188.142 310089.0023 2014379.253 203452.3046 916751.3666 92591.88802 155543.3833 15709.88171 1141381.483 115279.5298 1990016.323 200991.6486 2664201.993 269084.4013 3141886.317 317330.5181 3416435.281 345059.9634 3495509.041 353046.4131 3398838.844 343282.7232 3155241.299 318679.3712 2799245.486 282723.7941 2367700.338 239137.7341 1896681.517 191564.8332 1418939.998 143312.9398 962042.1766 97166.25984 547256.9948 55272.95648 189160.8925 19105.25014 104135.3169 10517.66701 330277.5365 33358.03119 491637.7715 49655.41493 594121.1961 60006.2408 645952.4486 65241.19731 656553.6007 66311.91367 635591.7078 64194.76249 592239.073 59816.14638 534658.3646 54000.49483 469700.1149 47439.7116 402783.0852 40681.09161 337918.4636 34129.76482 277835.9353 28061.42946 224171.8651 22641.35838 177685.4645 17946.23192 138476.2807 13986.10435106184.2851 10724.61279 80161.23333 8096.284566 59608.1912 6020.427311 43678.865 4411.565365 31551.60476 3186.71208 22474.81999 2269.956819 15791.31627 1594.922943 10947.0234 1105.649363 7489.028652 756.3918938 5056.994608 510.7564554 3371.118743 170.2414965Cumulative normalization
169.5485169 1.28191E-05 678.2902601 5.12838E-05 1431.795091 0.000108254 2533.367535 0.000191541 4122.619348 0.000311701 6384.808836 0.000482739 9561.051855 0.000722887 13958.73993 0.001055384 19961.08983 0.001509207 28034.25343 0.002119598 38729.86438 0.002928266 52680.34167 0.003983025 70583.78995 0.005336659 93175.04439 0.007044726 121179.4405 0.009162066 155246.399 0.011737781 195861.0542 0.014808551 243234.0361 0.018390301 297172.2019 0.022468427 356936.5539 0.026987056 421097.5908 0.031838107 487402.5773 0.036851257 552673.1675 0.041786199 612754.809 0.046328817 662540.6362 0.050092996 696091.3657 0.05262968 706868.3778 0.053444502 725647.4132 0.054864337 780532.3387 0.059014045 877259.9797 0.066327374 1020101.612 0.077127263 1211186.958 0.091574735 1449867.407 0.109620751 1732190.885 0.130966504 2050563.844 0.155037865 2393670.31 0.180979264 2746702.898 0.207671151 3091936.328 0.233773364 3409641.807 0.257794259 3679303.538 0.27818269 

## ( ) 2 () () f a f x f b        3881060.699 0.293437031 3997264.193 0.302222878 4014012.157 0.303489149 4105508.361 0.310406942 4307872.298 0.325707159 4616948.724 0.349075634 5021715.394 0.379679002 5504758.868 0.416200679 6043296.581 0.456918132 6610670.661 0.499815828 7178188.51 0.542724395 7717147.352 0.583473689 8200859.701 0.620045937 8606496.611 0.650715102 8916585.613 0.674160135 9120037.918 0.689542641 9212629.806 0.696543276 9228339.687 0.69773106 9343619.217 0.706447049 9544610.866 0.721643511 9813695.267 0.741988292 10131025.78 0.765980837 10476085.75 0.792069935 10829132.16 0.818762867 11172414.88 0.844717592 11491094.26 0.868812121 11773818.05 0.89018814 12012955.78 0.90826873 12204520.62 0.922752455 12347833.56 0.933587979 12444999.82 0.94093447 12500272.77 0.945113516 12519378.02 0.946558015 12529895.69 0.947353229 12563253.72 0.949875344 12612909.14 0.953629662 12672915.38 0.95816658 12738156.57 0.963099299 12804468.49 0.968112973 12868663.25 0.972966574 12928479.4 0.977489119 12982479.89 0.981571958 13029919.6 0.985158753 13070600.7 0.988234545 13104730.46 0.990815009 13132791.89 0.992936662 13155433.25 0.994648517 13173379.48 0.996005385 13187365.58 0.99706283913198090.2 0.997873699 13206186.48 0.998485838 13212206.91 0.998941027 13216618.47 0.999274575 13219805.19 0.999515514 13222075.14 0.999687139 13223670.07 0.999807727 13224775.72 0.999891323 13225532.11 0.999948511 13226042.86 0.999987128 13226213.11 1 667865176.8Raw Data: Sanitaryware - Tunnel Kiln - TEQ ng/dscm @ 7% O2 Runs TK #10 POC + RCE stacks 1 2.87E-01 2 2.19E-01 3 1.99E-01 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 2.35E-01 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.37 1.25 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs TK #10 POC + RCE stacks 1 -1.25E+00 2 -1.52E+00 3 -1.62E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate -1.46E+00

0.036209387 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 S-TK-TEQ 12/1/20143.610663737
0.004078839

887.2184741
7. Calculate 0.336681942

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 0.23616946
b- Calculate 0.055776014

c- Calculate 0.036872931

d-calculate 0.012397575

e- Calculate 0.111325

f- Calculate UPL 3.65E-01 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 S-TK-TEQ 12/1/2014∆z z

0.101 887.2185 0.336682

-5=f(a) 17605.51 1 -4.899 16022 2 -4.798 14542.2 3 -4.697 13161.72 4 -4.596 11876.2 5 -4.495 10681.44 6 -4.394 9573.284 7 -4.293 8547.685 8 -4.192 7600.685 9 -4.091 6728.422 10 -3.99 5927.123 11 -3.889 5193.107 12 -3.788 4522.785 13 -3.687 3912.661 14 -3.586 3359.33 15 -3.485 2859.479 16 -3.384 2409.889 17 -3.283 2007.431 18 -3.182 1649.068 19 -3.081 1331.855 20 -2.98 1052.941 21 -2.879 809.5638 22 -2.778 599.0562 23 -2.677 418.8415 24 -2.576 266.4351 25 -2.475 139.4446 26 -2.374 35.56968 27 -2.273 -47.3982 28 -2.172 -111.575 29 -2.071 -158.986 30 -1.97 -191.563 31 -1.869 -211.146 32 -1.768 -219.484 33 -1.667 -218.233 34 -1.566 -208.957 35 -1.465 -193.129 36 -1.364 -172.129 37 -1.263 -147.245 38 -1.162 -119.673 39 -1.061 -90.5184

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -60.7927

41 -0.859 -31.4161 42 -0.758 -3.21699 43 -0.657 23.06851 44 -0.556 46.79617 45 -0.455 67.41383 46 -0.354 84.46131 47 -0.253 97.57045 48 -0.152 106.4651 49 -0.051 110.9612 50 0.05 110.9665 51 0.151 106.481 52 0.252 97.59651 53 0.353 84.49703 54 0.454 67.45845 55 0.555 46.84871 56 0.656 23.12777 57 0.757 -3.1524 58 0.858 -31.3478 59 0.959 -60.7226 60 1.06 -90.4485 61 1.161 -119.606 62 1.262 -147.182 63 1.363 -172.074 64 1.464 -193.085 65 1.565 -208.927 66 1.666 -218.22 67 1.767 -219.492 68 1.868 -211.178 69 1.969 -191.624 70 2.07 -159.08 71 2.171 -111.706 72 2.272 -47.571 73 2.373 35.35002 74 2.474 139.1731 75 2.575 266.1063 76 2.676 418.4499 77 2.777 598.5961 78 2.878 809.0291 79 2.979 1052.325 80 3.08 1331.152 81 3.181 1648.271 82 3.282 2006.534 83 3.383 2408.885 84 3.484 2858.36 85 3.585 3358.088 86 3.686 3911.289 87 3.787 4521.275 88 3.888 5191.4589 3.989 5925.312

90 4.09 6726.448 91 4.191 7598.539 92 4.292 8545.358 93 4.393 9570.767 94 4.494 10678.72 95 4.595 11873.28 96 4.696 13158.57 97 4.797 14538.83 98 4.898 16018.38 99 4.999 17601.65distribution of Z Normal distribution

1.48672E-06 0.026174458 2.45094E-06 0.039268952 3.9995E-06 0.058161586 6.46025E-06 0.085027928 1.03291E-05 0.12267037 1.63472E-05 0.174612169 2.56093E-05 0.245164733 3.97118E-05 0.33944365 6.09553E-05 0.463301697 9.26132E-05 0.623140642 0.000139285 0.825559206 0.000207351 1.076794276 0.000305546 1.381918343 0.000445674 1.743770679 0.000643469 2.161624805 0.000919619 2.629631696 0.001300942 3.135126544 0.001821704 3.656944495 0.002525035 4.163952607 0.003464389 4.614063516 0.004704958 4.954040402 0.006324913 5.120420174 0.008416337 5.041859407 0.011085658 4.643133802 0.014453386 3.850889559 0.018652949 2.601053709 0.023828414 0.847569168 0.030130931 -1.428150627 0.03771375 -4.207922039 0.046725789 -7.428748381 0.057303789 -10.97727572 0.069563239 -14.68799766 0.083588399 -18.34630149 0.099421884 -21.69710668 0.117054396 -24.45932762 0.136415346 -26.34573356 0.157365126 -27.08704299 0.179689839 -26.45836928 0.203099244 -24.30553195 0.227228529 -20.56837045 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -15.29813113 0.275855243 -8.666299915 0.299326439 -0.96292955 0.321498297 7.416485128 0.341807853 15.99529887 0.359712192 24.24957629 0.37471238 31.64869828 0.386376486 37.69892943 0.394360216 41.9856079 0.398423793 44.2095716 0.398443914 44.21392378 0.394419966 41.99822077 0.386474058 37.71851907 0.374844865 31.6732761 0.359875719 24.27665692 0.34199778 16.0221556 0.32170943 7.440423246 0.299553264 -0.94431222 0.276092166 -8.654893328 0.25188591 -15.29515592 0.227469632 -20.57429664 0.203335281 -24.32007705 0.17991684 -26.48057001 0.157579839 -27.115387 0.136615273 -26.3783319 0.117237788 -24.49410634 0.099587708 -21.73199573 0.083736272 -18.37940249 0.069693339 -14.71771614 0.05741676 -11.00240962 0.046822635 -7.448530149 0.037795734 -4.222017161 0.030199481 -1.436619466 0.023885038 0.844336633 0.018699163 2.602419502 0.014490659 3.856055223 0.011115369 4.651224709 0.008439746 5.051998886 0.006343145 5.131788893 0.004718997 4.965918877 0.003475077 4.625857719 0.002533081 4.175204294 0.001827693 3.667328948 0.001305351 3.144440968 0.000922829 2.637777577 0.00064578 2.168587251 0.00044732 1.749597231 0.000306705 1.386699139 0.000208159 1.0806447740.000139842 0.828606121 9.29928E-05 0.625511251 6.12113E-05 0.465116345 3.98826E-05 0.340811039 2.5722E-05 0.246179489 1.64209E-05 0.175354117 1.03767E-05 0.123205036 6.49066E-06 0.085407785 4.01874E-06 0.058427725 2.46298E-06 0.039452881 1.49417E-06 0.026299871Absolute values

0.026174458 0.00132181 0.039268952 0.003966164 0.058161586 0.00587432 0.085027928 0.008587821 0.12267037 0.012389707 0.174612169 0.017635829 0.245164733 0.024761638 0.33944365 0.034283809 0.463301697 0.046793471 0.623140642 0.062937205 0.825559206 0.08338148 1.076794276 0.108756222 1.381918343 0.139573753 1.743770679 0.176120839 2.161624805 0.218324105 2.629631696 0.265592801 3.135126544 0.316647781 3.656944495 0.369351394 4.163952607 0.420559213 4.614063516 0.466020415 4.954040402 0.500358081 5.120420174 0.517162438 5.041859407 0.5092278 4.643133802 0.468956514 3.850889559 0.388939845 2.601053709 0.262706425 0.847569168 0.085604486 1.428150627 0.144243213 4.207922039 0.425000126 7.428748381 0.750303587 10.97727572 1.108704848 14.68799766 1.483487763 18.34630149 1.852976451 21.69710668 2.191407775 24.45932762 2.47039209 26.34573356 2.660919089 27.08704299 2.735791342 26.45836928 2.672295297 24.30553195 2.454858726 20.56837045 2.077405415 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 15.29813113 1.545111244 8.666299915 0.875296291 0.96292955 0.097255885 7.416485128 0.749064998 15.99529887 1.615525186 24.24957629 2.449207205 31.64869828 3.196518526 37.69892943 3.807591873 41.9856079 4.240546398 44.2095716 4.465166731 44.21392378 4.465606302 41.99822077 4.241820298 37.71851907 3.809570426 31.6732761 3.199000886 24.27665692 2.451942349 16.0221556 1.618237715 7.440423246 0.751482748 0.94431222 0.095375534 8.654893328 0.874144226 15.29515592 1.544810748 20.57429664 2.07800396 24.32007705 2.456327782 26.48057001 2.674537571 27.115387 2.738654087 26.3783319 2.664211522 24.49410634 2.47390474 21.73199573 2.194931569 18.37940249 1.856319652 14.71771614 1.48648933 11.00240962 1.111243372 7.448530149 0.752301545 4.222017161 0.426423733 1.436619466 0.145098566 0.844336633 0.085278 2.602419502 0.26284437 3.856055223 0.389461578 4.651224709 0.469773696 5.051998886 0.510251888 5.131788893 0.518310678 4.965918877 0.501557807 4.625857719 0.46721163 4.175204294 0.421695634 3.667328948 0.370400224 3.144440968 0.317588538 2.637777577 0.266415535 2.168587251 0.219027312 1.749597231 0.17670932 1.386699139 0.140056613 1.080644774 0.1091451220.828606121 0.083689218 0.625511251 0.063176636 0.465116345 0.046976751 0.340811039 0.034421915 0.246179489 0.024864128 0.175354117 0.017710766 0.123205036 0.012443709 0.085407785 0.008626186 0.058427725 0.0059012 0.039452881 0.003984741 0.026299871 0.001328143Cumulative normalization
0.00132181 1.28052E-05 0.005287974 5.12281E-05 0.011162294 0.000108136 0.019750115 0.000191332 0.032139822 0.000311359 0.049775652 0.000482209 0.07453729 0.000722091 0.108821098 0.001054221 0.15561457 0.00150754 0.218551774 0.002117253 0.301933254 0.002925024 0.410689476 0.003978616 0.550263229 0.005330758 0.726384067 0.007036955 0.944708173 0.009152003 1.210300974 0.011724974 1.526948755 0.014792547 1.896300149 0.018370694 2.316859362 0.022444925 2.782879777 0.026959569 3.283237858 0.031806863 3.800400295 0.036816952 4.309628096 0.041750174 4.77858461 0.046293261 5.167524455 0.050061174 5.43023088 0.052606183 5.515835366 0.053435489 5.660078579 0.054832867 6.085078705 0.05895012 6.835382291 0.066218799 7.94408714 0.076959545 9.427574903 0.091331057 11.28055135 0.109282047 13.47195913 0.130511641 15.94235122 0.154443938 18.60327031 0.180221994 21.33906165 0.206725386 24.01135695 0.232613651 26.46621567 0.256395466 28.54362109 0.276520645 

## ( ) 2 () () f a f x f b        30.08873233 0.291489144 30.96402862 0.299968709 31.06128451 0.30091089 31.81034951 0.30816757 33.42587469 0.323818215 35.8750819 0.34754528 39.07160042 0.378512036 42.8791923 0.415398658 47.11973869 0.456479593 51.58490542 0.499736571 56.05051173 0.542997807 60.29233202 0.584091082 64.10190245 0.620996872 67.30090334 0.651987677 69.75284569 0.675741239 71.3710834 0.691418161 72.12256615 0.698698264 72.21794168 0.699622229 73.09208591 0.708090633 74.63689666 0.723056221 76.71490062 0.743187199 79.1712284 0.766983245 81.84576597 0.792893232 84.58442006 0.819424358 87.24863158 0.84523431 89.72253632 0.869200636 91.91746789 0.890464367 93.77378754 0.908447745 95.26027687 0.922848335 96.37152024 0.933613673 97.12382179 0.940901708 97.55024552 0.945032752 97.69534409 0.946438417 97.78062209 0.94726456 98.04346646 0.949810905 98.43292803 0.953583873 98.90270173 0.958134876 99.41295362 0.963078019 99.93126429 0.968099232 100.4328221 0.972958149 100.9000337 0.977484332 101.3217294 0.981569572 101.6921296 0.985157881 102.0097181 0.988234568 102.2761337 0.990815508 102.495161 0.992937369 102.6718703 0.994649267 102.8119269 0.996006086 102.921072 0.997063446103.0047612 0.997874198 103.0679379 0.998486231 103.1149146 0.998941326 103.1493365 0.999274793 103.1742007 0.999515668 103.1919114 0.999687244 103.2043552 0.999807794 103.2129813 0.999891362 103.2188825 0.999948531 103.2228673 0.999987133 103.2241954 1 5211.862942Raw Data: Sanitaryware - Manual Glaze Application - PM lb/ton Runs SO3/SO4 1 3.52E+00 2 3.17E+00 3 3.29E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 3.33E+00 Result Kurtosis #DIV/0! #DIV/0! Skewness 0.88 0.82 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs SO3/SO4 1 1.26E+00 2 1.16E+00 3 1.19E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate 1.20E+00

0.00272611 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 S-Manual-PM 12/1/20143.043789176
2.23559E-05

136153.433
7. Calculate 0.090578141

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 3.330813203
b- Calculate 11.09431659

c- Calculate 0.00272983

d-calculate 0.000910561

e- Calculate 0.426351

f- Calculate UPL 3.83E+00 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 S-Manual-PM 12/1/2014∆z z

0.101 136153.4 0.090578

-5=f(a) 2711662 1 -4.899 2467774 2 -4.798 2239859 3 -4.697 2027237 4 -4.596 1829243 5 -4.495 1645224 6 -4.394 1474543 7 -4.293 1316576 8 -4.192 1170714 9 -4.091 1036363 10 -3.99 912939.8 11 -3.889 799879.3 12 -3.788 696628.4 13 -3.687 602648.6 14 -3.586 517415.7 15 -3.485 440419.6 16 -3.384 371164.3 17 -3.283 309168 18 -3.182 253963.1 19 -3.081 205096.3 20 -2.98 162128.1 21 -2.879 124633.6 22 -2.778 92201.7 23 -2.677 64435.71 24 -2.576 40953.02 25 -2.475 21385.19 26 -2.374 5377.953 27 -2.273 -7408.79 28 -2.172 -17301 29 -2.071 -24610.3 30 -1.97 -29634.5 31 -1.869 -32656.9 32 -1.768 -33946.8 33 -1.667 -33759.3 34 -1.566 -32335.2 35 -1.465 -29901.4 36 -1.364 -26670.5 37 -1.263 -22840.8 38 -1.162 -18596.6 39 -1.061 -14108

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -9530.94

41 -0.859 -5007.14 42 -0.758 -664.182 43 -0.657 3384.516 44 -0.556 7039.711 45 -0.455 10216.33 46 -0.354 12843.45 47 -0.253 14864.34 48 -0.152 16236.43 49 -0.051 16931.31 50 0.05 16934.74 51 0.151 16246.66 52 0.252 14881.15 53 0.353 12866.48 54 0.454 10245.1 55 0.555 7073.592 56 0.656 3422.736 57 0.757 -622.533 58 0.858 -4963.11 59 0.959 -9485.72 60 1.06 -14062.9 61 1.161 -18553.1 62 1.262 -22800.5 63 1.363 -26635.2 64 1.464 -29873 65 1.565 -32315.7 66 1.666 -33750.8 67 1.767 -33951.8 68 1.868 -32677.7 69 1.969 -29673.8 70 2.07 -24670.7 71 2.171 -17385.4 72 2.272 -7520.25 73 2.373 5236.304 74 2.474 21210.06 75 2.575 40740.97 76 2.676 64183.17 77 2.777 91904.95 78 2.878 124288.8 79 2.979 161731.3 80 3.08 204643.3 81 3.181 253449.7 82 3.282 308589.7 83 3.383 370516.5 84 3.484 439697.7 85 3.585 516614.9 86 3.686 601763.9 87 3.787 695654.6 88 3.888 798811.389 3.989 911772.1

90 4.09 1035090 91 4.191 1169331 92 4.292 1315076 93 4.393 1472920 94 4.494 1643472 95 4.595 1827356 96 4.696 2025209 97 4.797 2237683 98 4.898 2465443 99 4.999 2709170distribution of Z Normal distribution

1.48672E-06 4.031481005 2.45094E-06 6.048365247 3.9995E-06 8.958322361 6.46025E-06 13.09645398 1.03291E-05 18.89441226 1.63472E-05 26.89488357 2.56093E-05 37.76195168 3.97118E-05 52.28356041 6.09553E-05 71.3611878 9.26132E-05 95.98084062 0.000139285 127.1588042 0.000207351 165.8555296 0.000305546 212.8519519 0.000445674 268.5847654 0.000643469 332.9410422 0.000919619 405.0182615 0.001300942 482.8632665 0.001821704 563.2125411 0.002525035 641.2657272 0.003464389 710.5332793 0.004704958 762.805953 0.006324913 788.2965098 0.008416337 776.0005805 0.011085658 714.312285 0.014453386 591.9098322 0.018652949 398.8968556 0.023828414 128.1480907 0.030130931 -223.2337352 0.03771375 -652.4844322 0.046725789 -1149.937971 0.057303789 -1698.170467 0.069563239 -2271.72114 0.083588399 -2837.558632 0.099421884 -3356.408468 0.117054396 -3784.977645 0.136415346 -4079.010797 0.157365126 -4196.999161 0.179689839 -4104.252546 0.203099244 -3776.951758 0.227228529 -3205.740627 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -2398.406597 0.275855243 -1381.245114 0.299326439 -198.8071609 0.321498297 1088.116162 0.341807853 2406.228512 0.359712192 3674.936935 0.37471238 4812.600058 0.386376486 5743.233362 0.394360216 6403.003714 0.398423793 6745.837944 0.398443914 6747.545402 0.394419966 6408.005158 0.386474058 5751.17698 0.374844865 4822.934858 0.359875719 3686.961705 0.34199778 2419.152737 0.32170943 1101.12645 0.299553264 -186.4819206 0.276092166 -1370.276165 0.25188591 -2389.320434 0.227469632 -3198.890238 0.203335281 -3772.505416 0.17991684 -4102.199631 0.157579839 -4197.170717 0.136615273 -4081.111259 0.117237788 -3788.623394 0.099587708 -3361.168725 0.083736272 -2842.994537 0.069693339 -2277.419639 0.05741676 -1703.770674 0.046822635 -1155.148797 0.037795734 -657.0933561 0.030199481 -227.1075141 0.023885038 125.0693275 0.018699163 396.6102932 0.014490659 590.3635011 0.011115369 713.4196203 0.008439746 775.6544861 0.006343145 788.3817932 0.004718997 763.2094176 0.003475077 711.1511603 0.002533081 642.0084875 0.001827693 564.0072941 0.001305351 483.6542486 0.000922829 405.7658469 0.00064578 333.619795 0.00044732 269.1809725 0.000306705 213.3609994 0.000208159 166.27939150.000139842 127.5038211 9.29928E-05 96.25588068 6.12113E-05 71.57622068 3.98826E-05 52.44862548 2.5722E-05 37.88647264 1.64209E-05 26.9872667 1.03767E-05 18.96186169 6.49066E-06 13.14494148 4.01874E-06 8.992657936 2.46298E-06 6.072325546 1.49417E-06 4.047963456Absolute values

4.031481005 0.203589791 6.048365247 0.61088489 8.958322361 0.904790558 13.09645398 1.322741852 18.89441226 1.908335639 26.89488357 2.716383241 37.76195168 3.81395712 52.28356041 5.280639602 71.3611878 7.207479968 95.98084062 9.694064903 127.1588042 12.84303922 165.8555296 16.75140849 212.8519519 21.49804715 268.5847654 27.1270613 332.9410422 33.62704526 405.0182615 40.90684442 482.8632665 48.76918992 563.2125411 56.88446665 641.2657272 64.76783845 710.5332793 71.76386121 762.805953 77.04340126 788.2965098 79.61794749 776.0005805 78.37605863 714.312285 72.14554078 591.9098322 59.78289306 398.8968556 40.28858242 128.1480907 12.94295716 223.2337352 22.54660726 652.4844322 65.90092765 1149.937971 116.1437351 1698.170467 171.5152171 2271.72114 229.4438351 2837.558632 286.5934218 3356.408468 338.9972553 3784.977645 382.2827422 4079.010797 411.9800905 4196.999161 423.8969152 4104.252546 414.5295072 3776.951758 381.4721275 3205.740627 323.7798033 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 2398.406597 242.2390663 1381.245114 139.5057565 198.8071609 20.07952325 1088.116162 109.8997324 2406.228512 243.0290797 3674.936935 371.1686304 4812.600058 486.0726059 5743.233362 580.0665696 6403.003714 646.7033751 6745.837944 681.3296324 6747.545402 681.5020856 6408.005158 647.208521 5751.17698 580.868875 4822.934858 487.1164206 3686.961705 372.3831322 2419.152737 244.3344265 1101.12645 111.2137715 186.4819206 18.83467398 1370.276165 138.3978926 2389.320434 241.3213639 3198.890238 323.087914 3772.505416 381.023047 4102.199631 414.3221628 4197.170717 423.9142425 4081.111259 412.1922371 3788.623394 382.6509628 3361.168725 339.4780413 2842.994537 287.1424482 2277.419639 230.0193835 1703.770674 172.0808381 1155.148797 116.6700285 657.0933561 66.36642897 227.1075141 22.93785892 125.0693275 12.63200207 396.6102932 40.05763962 590.3635011 59.62671361 713.4196203 72.05538166 775.6544861 78.3411031 788.3817932 79.62656111 763.2094176 77.08415118 711.1511603 71.82626719 642.0084875 64.84285724 564.0072941 56.96473671 483.6542486 48.8490791 405.7658469 40.98235053 333.619795 33.6955993 269.1809725 27.18727823 213.3609994 21.54946094 166.2793915 16.79421855127.5038211 12.87788593 96.25588068 9.721843948 71.57622068 7.229198289 52.44862548 5.297311174 37.88647264 3.826533737 26.9872667 2.725713937 18.96186169 1.915148031 13.14494148 1.327639089 8.992657936 0.908258451 6.072325546 0.61330488 4.047963456 0.204422155Cumulative normalization
0.203589791 1.28191E-05 0.814474681 5.12835E-05 1.719265239 0.000108254 3.042007091 0.00019154 4.95034273 0.000311699 7.66672597 0.000482736 11.48068309 0.000722883 16.76132269 0.001055379 23.96880266 0.001509199 33.66286756 0.002119587 46.50590679 0.002928251 63.25731527 0.003983006 84.75536242 0.005336633 111.8824237 0.007044692 145.509469 0.009162024 186.4163134 0.011737729 235.1855033 0.014808487 292.06997 0.018390226 356.8378084 0.022468341 428.6016696 0.026986963 505.6450709 0.031838011 585.2630184 0.036851166 663.639077 0.041786125 735.7846178 0.046328779 795.5675109 0.050093017 835.8560933 0.052629793 848.7990504 0.053444748 871.3456577 0.054864398 937.2465853 0.059013859 1053.39032 0.066326866 1224.905538 0.077126345 1454.349373 0.091573307 1740.942795 0.109618701 2079.94005 0.13096371 2462.222792 0.155034195 2874.202882 0.180974578 3298.099798 0.207665305 3712.629305 0.233766212 4094.101432 0.257785657 4417.881236 0.278172496 

## ( ) 2 () () f a f x f b        4660.120302 0.293425112 4799.626058 0.302209111 4819.705582 0.303473421 4929.605314 0.310393273 5172.634394 0.325695632 5543.803024 0.349066316 6029.87563 0.379671944 6609.9422 0.416195915 7256.645575 0.456915681 7937.975207 0.499815694 8619.477293 0.542726566 9266.685814 0.58347814 9847.554689 0.620052628 10334.67111 0.65072398 10707.05424 0.674171135 10951.38867 0.689555685 11062.60244 0.696558275 11081.43711 0.697744203 11219.83501 0.706458446 11461.15637 0.721653278 11784.24428 0.741996553 12165.26733 0.765987721 12579.58949 0.792075573 13003.50374 0.818767391 13415.69597 0.844721132 13798.34694 0.868814802 14137.82498 0.890190083 14424.96743 0.908270047 14654.98681 0.922753249 14827.06765 0.933588342 14943.73768 0.940934486 15010.1041 0.945113258 15033.04196 0.946557543 15045.67397 0.947352919 15085.73161 0.949875154 15145.35832 0.953629558 15217.4137 0.958166535 15295.7548 0.963099293 15375.38136 0.96811299 15452.46552 0.972966604 15524.29178 0.977489155 15589.13464 0.981571994 15646.09938 0.985158787 15694.94846 0.988234576 15735.93081 0.990815035 15769.62641 0.992936683 15796.81368 0.994648534 15818.36315 0.996005399 15835.15736 0.99706284915848.03525 0.997873707 15857.75709 0.998485844 15864.98629 0.998941031 15870.2836 0.999274577 15874.11014 0.999515516 15876.83585 0.999687141 15878.751 0.999807728 15880.07864 0.999891323 15880.9869 0.999948512 15881.6002 0.999987129 15881.80462 1 801960.6529Raw Data: Sanitaryware - Spray Machine Glaze Application - PM lb/ton Runs EO14 (EPN014-Bowl SM 1) 1 2.14E+00 2 1.72E+00 3 2.01E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 3.00 Kurtosis #DIV/0! SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness -1.02 SE Skewness 1.22 Result Raw Data Result Skewness normal #DIV/0!
ni = number test runs = 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 1
n =Total # test runs = 3

2

This step is for QC only: means 1.95E+00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1.95E+00 Mean =

Pooled Variance = 4.67E-02

m= number future runs = 3
Term1 6.67E-01

Term2 3.11E-02

Squared root Term2 1.76E-01 NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 6.964556734
UPL POOLED VARIANCE = 3.18E+00 Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 S-SprayMachine-PM 12/1/2014Raw Data: Sanitaryware - Robot Glaze Application - PM lb/ton Runs SR1 (EPN 104-1P) 1 1.68E+00 2 1.17E+00 3 1.10E+00 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 1.32E+00 Result Kurtosis #DIV/0! #DIV/0! Skewness 1.62 1.57 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs SR1 (EPN 104-1P) 1 5.21E-01 2 1.61E-01 3 9.41E-02 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3

3. Calculate 2.59E-01

0.052842818 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 S-Robot-PM 12/1/20143.913358704
0.008833719

445.0023834
7. Calculate 0.41077265

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 1.330015688
b- Calculate 1.768941731

c- Calculate 0.054263921

d-calculate 0.018312364

e- Calculate 0.761256

f- Calculate UPL 2.21E+00 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula a- Numerator first term
b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 S-Robot-PM 12/1/2014∆z z

0.101 445.0024 0.410773

-5=f(a) 8796.683 1 -4.899 8005.405 2 -4.798 7265.963 3 -4.697 6576.149 4 -4.596 5933.801 5 -4.495 5336.805 6 -4.394 4783.09 7 -4.293 4270.633 8 -4.192 3797.456 9 -4.091 3361.627 10 -3.99 2961.262 11 -3.889 2594.52 12 -3.788 2259.609 13 -3.687 1954.779 14 -3.586 1678.33 15 -3.485 1428.606 16 -3.384 1203.998 17 -3.283 1002.941 18 -3.182 823.9184 19 -3.081 665.4583 20 -2.98 526.135 21 -2.879 404.5689 22 -2.778 299.4263 23 -2.677 209.4195 24 -2.576 133.307 25 -2.475 69.89296 26 -2.374 18.02778 27 -2.273 -23.3922 28 -2.172 -55.4248 29 -2.071 -79.0816 30 -1.97 -95.3283 31 -1.869 -105.085 32 -1.768 -109.224 33 -1.667 -108.575 34 -1.566 -103.918 35 -1.465 -95.9904 36 -1.364 -85.4806 37 -1.263 -73.0327 38 -1.162 -59.2445 39 -1.061 -44.6678

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 -29.8082

41 -0.859 -15.1256 42 -0.758 -1.03369 43 -0.657 12.09978 44 -0.556 23.95301 45 -0.455 34.25024 46 -0.354 42.76169 47 -0.253 49.30358 48 -0.152 53.7381 49 -0.051 55.97348 50 0.05 55.9639 51 0.151 53.70957 52 0.252 49.25668 53 0.353 42.6974 54 0.454 34.16993 55 0.555 23.85844 56 0.656 11.99309 57 0.757 -1.14994 58 0.858 -15.2485 59 0.959 -29.9344 60 1.06 -44.7936 61 1.161 -59.3658 62 1.262 -73.145 63 1.363 -85.579 64 1.464 -96.0696 65 1.565 -103.973 66 1.666 -108.598 67 1.767 -109.21 68 1.868 -105.027 69 1.969 -95.2188 70 2.07 -78.913 71 2.171 -55.1892 72 2.272 -23.0811 73 2.373 18.42318 74 2.474 70.38183 75 2.575 133.8989 76 2.676 210.1245 77 2.777 300.2546 78 2.878 405.5313 79 2.979 527.2427 80 3.08 666.7228 81 3.181 825.3517 82 3.282 1004.555 83 3.383 1205.806 84 3.484 1430.621 85 3.585 1680.566 86 3.686 1957.249 87 3.787 2262.327 88 3.888 2597.50289 3.989 2964.522

90 4.09 3365.181 91 4.191 3801.318 92 4.292 4274.821 93 4.393 4787.621 94 4.494 5341.695 95 4.595 5939.068 96 4.696 6581.81 97 4.797 7272.037 98 4.898 8011.911 99 4.999 8803.639distribution of Z Normal distribution

1.48672E-06 0.013078201 2.45094E-06 0.019620766 3.9995E-06 0.029060239 6.46025E-06 0.042483545 1.03291E-05 0.061290758 1.63472E-05 0.087242068 2.56093E-05 0.122491391 3.97118E-05 0.169594361 6.09553E-05 0.231474862 9.26132E-05 0.311331014 0.000139285 0.412459327 0.000207351 0.537975608 0.000305546 0.690414156 0.000445674 0.871194011 0.000643469 1.079953604 0.000919619 1.313773542 0.001300942 1.56633144 0.001821704 1.827061505 0.002525035 2.080422425 0.003464389 2.305406221 0.004704958 2.475442692 0.006324913 2.558862722 0.008416337 2.520072443 0.011085658 2.321553371 0.014453386 1.926737401 0.018652949 1.303709889 0.023828414 0.429573486 0.030130931 -0.704829979 0.03771375 -2.09027684 0.046725789 -3.695148895 0.057303789 -5.462671206 0.069563239 -7.310024956 0.083588399 -9.129880838 0.099421884 -10.79472745 0.117054396 -12.16410983 0.136415346 -13.09456353 0.157365126 -13.45166219 0.179689839 -13.1232363 0.203099244 -12.03252038 0.227228529 -10.14979695 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 -7.501073506 0.275855243 -4.172479605 0.299326439 -0.309410026 0.321498297 3.890057793 0.341807853 8.18732786 0.359712192 12.32023057 0.37471238 16.02333601 0.386376486 19.04974229 0.394360216 21.19216922 0.398423793 22.30116466 0.398443914 22.29847568 0.394419966 21.18412711 0.386474058 19.03642773 0.374844865 16.00490254 0.359875719 12.29692901 0.34199778 8.159532851 0.32170943 3.858290395 0.299553264 -0.344469529 0.276092166 -4.209993231 0.25188591 -7.540064044 0.227469632 -10.18918348 0.203335281 -12.07116845 0.17991684 -13.16001836 0.157579839 -13.48552206 0.136615273 -13.12457851 0.117237788 -12.18954394 0.099587708 -10.81507064 0.083736272 -9.144870707 0.069693339 -7.319649489 0.05741676 -5.467153308 0.046822635 -3.694915216 0.037795734 -2.08591484 0.030199481 -0.697037982 0.023885038 0.44003835 0.018699163 1.316081305 0.014490659 1.940283374 0.011115369 2.335610987 0.008439746 2.534072515 0.006343145 2.572344056 0.004718997 2.488056719 0.003475077 2.316913432 0.002533081 2.090682518 0.001827693 1.836019268 0.001305351 1.574000364 0.000922829 1.320218888 0.00064578 1.085276294 0.00044732 0.875516308 0.000306705 0.693867728 0.000208159 0.5406921880.000139842 0.414563943 9.29928E-05 0.312937549 6.12113E-05 0.232683571 3.98826E-05 0.170490958 2.5722E-05 0.123147285 1.64209E-05 0.087715363 1.03767E-05 0.061627722 6.49066E-06 0.042720286 4.01874E-06 0.029224401 2.46298E-06 0.019733138 1.49417E-06 0.013154142Absolute values

0.013078201 0.000660449 0.019620766 0.001981697 0.029060239 0.002935084 0.042483545 0.004290838 0.061290758 0.006190367 0.087242068 0.008811449 0.122491391 0.01237163 0.169594361 0.01712903 0.231474862 0.023378961 0.311331014 0.031444432 0.412459327 0.041658392 0.537975608 0.054335536 0.690414156 0.06973183 0.871194011 0.087990595 1.079953604 0.109075314 1.313773542 0.132691128 1.56633144 0.158199475 1.827061505 0.184533212 2.080422425 0.210122665 2.305406221 0.232846028 2.475442692 0.250019712 2.558862722 0.258445135 2.520072443 0.254527317 2.321553371 0.23447689 1.926737401 0.194600478 1.303709889 0.131674699 0.429573486 0.043386922 0.704829979 0.071187828 2.09027684 0.211117961 3.695148895 0.373210038 5.462671206 0.551729792 7.310024956 0.738312521 9.129880838 0.922117965 10.79472745 1.090267472 12.16410983 1.228575092 13.09456353 1.322550917 13.45166219 1.358617881 13.1232363 1.325446867 12.03252038 1.215284559 10.14979695 1.025129492 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 7.501073506 0.757608424 4.172479605 0.42142044 0.309410026 0.031250413 3.890057793 0.392895837 8.18732786 0.826920114 12.32023057 1.244343288 16.02333601 1.618356937 19.04974229 1.924023971 21.19216922 2.140409091 22.30116466 2.252417631 22.29847568 2.252146043 21.18412711 2.139596839 19.03642773 1.922679201 16.00490254 1.616495157 12.29692901 1.24198983 8.159532851 0.824112818 3.858290395 0.38968733 0.344469529 0.034791422 4.209993231 0.425209316 7.540064044 0.761546468 10.18918348 1.029107531 12.07116845 1.219188014 13.16001836 1.329161854 13.48552206 1.362037728 13.12457851 1.325582429 12.18954394 1.231143938 10.81507064 1.092322135 9.144870707 0.923631941 7.319649489 0.739284598 5.467153308 0.552182484 3.694915216 0.373186437 2.08591484 0.210677399 0.697037982 0.070400836 0.44003835 0.044443873 1.316081305 0.132924212 1.940283374 0.195968621 2.335610987 0.23589671 2.534072515 0.255941324 2.572344056 0.25980675 2.488056719 0.251293729 2.316913432 0.234008257 2.090682518 0.211158934 1.836019268 0.185437946 1.574000364 0.158974037 1.320218888 0.133342108 1.085276294 0.109612906 0.875516308 0.088427147 0.693867728 0.070080641 0.540692188 0.0546099110.414563943 0.041870958 0.312937549 0.031606692 0.232683571 0.023501041 0.170490958 0.017219587 0.123147285 0.012437876 0.087715363 0.008859252 0.061627722 0.0062244 0.042720286 0.004314749 0.029224401 0.002951665 0.019733138 0.001993047 0.013154142 0.000664284Cumulative normalization
0.000660449 1.27894E-05 0.002642147 5.11643E-05 0.005577231 0.000108001 0.009868069 0.000191092 0.016058435 0.000310966 0.024869884 0.000481597 0.037241515 0.00072117 0.054370545 0.001052868 0.077749506 0.001505594 0.109193939 0.002114505 0.150852331 0.002921206 0.205187867 0.003973395 0.274919697 0.005323729 0.362910292 0.007027638 0.471985606 0.009139845 0.604676734 0.011709365 0.762876209 0.014772846 0.947409421 0.018346271 1.157532086 0.022415227 1.390378114 0.026924213 1.640397826 0.031765762 1.898842961 0.036770467 2.153370278 0.041699305 2.387847168 0.046239872 2.582447646 0.050008246 2.714122344 0.052558083 2.757509267 0.053398257 2.828697094 0.054776785 3.039815055 0.058865015 3.413025094 0.066092104 3.964754885 0.07677617 4.703067406 0.091073348 5.625185371 0.108929858 6.715452843 0.130042527 7.944027935 0.153833479 9.266578852 0.17944424 10.62519673 0.205753427 11.9506436 0.231420268 13.16592816 0.254953853 14.19105765 0.274805147 

## ( ) 2 () () f a f x f b        14.94866607 0.289475984 15.37008651 0.297636652 15.40133693 0.298241805 15.79423276 0.305850104 16.62115288 0.321863139 17.86549617 0.345959436 19.4838531 0.377298384 21.40787707 0.414556473 23.54828616 0.456004788 25.8007038 0.499622112 28.05284984 0.543234177 30.19244668 0.584666763 32.11512588 0.621898811 33.73162104 0.653201706 34.97361087 0.677252429 35.79772368 0.693211102 36.18741101 0.700757268 36.22220244 0.701430993 36.64741175 0.709665031 37.40895822 0.724412127 38.43806575 0.744340455 39.65725377 0.767949628 40.98641562 0.793688408 42.34845335 0.820063819 43.67403578 0.845733286 44.90517971 0.869573982 45.99750185 0.890726439 46.92113379 0.908612267 47.66041839 0.922928269 48.21260087 0.9336211 48.58578731 0.940847733 48.79646471 0.944927431 48.86686554 0.94629072 48.91130942 0.947151361 49.04423363 0.949725394 49.24020225 0.953520262 49.47609896 0.958088324 49.73204028 0.963044543 49.99184703 0.968075615 50.24314076 0.972941835 50.47714902 0.977473328 50.68830795 0.981562351 50.8737459 0.985153295 51.03271994 0.988231775 51.16606204 0.990813901 51.27567495 0.992936519 51.3641021 0.994648881 51.43418274 0.99600597 51.48879265 0.99706347351.53066361 0.99787429 51.5622703 0.998486343 51.58577134 0.998941433 51.60299093 0.999274885 51.6154288 0.99951574 51.62428805 0.999687297 51.63051245 0.99980783 51.6348272 0.999891384 51.63777887 0.999948542 51.63977191 0.999987136 51.6404362 1 2607.000507Raw Data Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 0.00 Kurtosis #DIV/0! SE Kurtosis 0.00 Result Kurtosis #DIV/0! Skewness #DIV/0! SE Skewness 0.00 Result Raw Data Result Skewness #DIV/0! #DIV/0!
ni = number test runs = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 0
n =Total # test runs = 0

-1

This step is for QC only: means #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

#DIV/0! Mean =

Pooled Variance = #DIV/0!

m= number future runs = 3
Term1 #DIV/0!

Term2 #DIV/0!

Squared root Term2 #DIV/0! NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = #NUM!
UPL POOLED VARIANCE = #DIV/0! Use for large sample sets and small sample sets that are Normal.

 2 2 1 11n i i s xX n   

 1 1 1 i

n N ij i j X x n   

1 1 n m 

21 1 sn m        1 1 N i i df n

  
      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n  1

N i in

  N

2

, 1 1 dfp X t s n m    

   

09000064819365f6 UPL Pooled Template 12/1/2014Raw Data Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Logtransformed Data Sample Size 0.00 0.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis 0.00 0.00 Average of Raw Data #DIV/0! Result Kurtosis #DIV/0! #DIV/0! Skewness #DIV/0! #DIV/0! SE Skewness 0.00 0.00 Result Raw Data Result Log Data Result Skewness #DIV/0! #DIV/0! #DIV/0! #DIV/0! 1. Take LN( ) of Raw Data Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 0

3. Calculate #DIV/0!

#DIV/0! 4. Calculate

5. m= number future runs = 3 6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n i

i x n    2 2 1 ˆ 1

n i i x x n   


 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e          

09000064819365f6 Lognormal Template 12/1/2014#DIV/0! #DIV/0!

#DIV/0!
7. Calculate #DIV/0!

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate #DIV/0!
b- Calculate #DIV/0!

c- Calculate #DIV/0!

d-calculate #DIV/0!

e- Calculate #DIV/0!

f- Calculate UPL #DIV/0! 11. In column B, go down the the row number from Step 10. above, and copy the z value. 12. calculate the UPL using the formula b- denominator first term a- Numerator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e   

###   2 2 ˆ 1 m e



2z    2 2 ˆ ˆ 1 1 2

z e e

m      

2z

 1z 

2 ˆ 2 2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ ˆ 2 22 .99 ˆ ˆ

( 1) 2( 1) z UPL e me e m e

m n n                    

  

2 ˆ 2 ˆ e  
2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2( 1) n n       

  

2 2 2 2 4
ˆ ˆ ˆ ˆ ˆ 2 22 ˆ ˆ ( 1) 2( 1) me e me n n             

 

     2 2 2 ˆ 233 1 3 1 1 z e e e m

m e           



09000064819365f6 Lognormal Template 12/1/2014∆z z

0.101 23.80249 1.377354

-5=f(a) 390.0648 1 -4.899 354.4355 2 -4.798 321.1779 3 -4.697 290.1895 4 -4.596 261.37 5 -4.495 234.6213 6 -4.394 209.8473 7 -4.293 186.9542 8 -4.192 165.8504 9 -4.091 146.4462 10 -3.99 128.6545 11 -3.889 112.3899 12 -3.788 97.56945 13 -3.687 84.11235 14 -3.586 71.93989 15 -3.485 60.97555 16 -3.384 51.14496 17 -3.283 42.37594 18 -3.182 34.59846 19 -3.081 27.74465 20 -2.98 21.74883 21 -2.879 16.54744 22 -2.778 12.07914 23 -2.677 8.284705 24 -2.576 5.107107 25 -2.475 2.491468 26 -2.374 0.38508 27 -2.273 -1.2626 28 -2.172 -2.49996 29 -2.071 -3.37321 30 -1.97 -3.92639 31 -1.869 -4.20141 32 -1.768 -4.23797 33 -1.667 -4.07363 34 -1.566 -3.74379 35 -1.465 -3.28168 36 -1.364 -2.71835 37 -1.263 -2.0827 38 -1.162 -1.40147 39 -1.061 -0.69922

#   1 3 

## 1 3 6 24 z 

## z z      

     2z  1z



## 40 -0.96 0.001637

41 -0.859 0.68087 42 -0.758 1.320402 43 -0.657 1.904325 44 -0.556 2.418893 45 -0.455 2.852526 46 -0.354 3.19581 47 -0.253 3.441494 48 -0.152 3.584492 49 -0.051 3.621883 50 0.05 3.55291 51 0.151 3.378983 52 0.252 3.103674 53 0.353 2.73272 54 0.454 2.274026 55 0.555 1.737657 56 0.656 1.135845 57 0.757 0.482988 58 0.858 -0.20435 59 0.959 -0.90745 60 1.06 -1.60542 61 1.161 -2.2752 62 1.262 -2.89157 63 1.363 -3.42715 64 1.464 -3.85238 65 1.565 -4.13556 66 1.666 -4.2428 67 1.767 -4.13806 68 1.868 -3.78313 69 1.969 -3.13764 70 2.07 -2.15904 71 2.171 -0.80265 72 2.272 0.978414 73 2.373 3.233181 74 2.474 6.012847 75 2.575 9.370774 76 2.676 13.36249 77 2.777 18.04568 78 2.878 23.4802 79 2.979 29.72808 80 3.08 36.8535 81 3.181 44.92281 82 3.282 54.00452 83 3.383 64.16932 84 3.484 75.49004 85 3.585 88.04169 86 3.686 101.9015 87 3.787 117.1487 88 3.888 133.864889 3.989 152.1336

90 4.09 172.0408 91 4.191 193.6745 92 4.292 217.1248 93 4.393 242.484 94 4.494 269.8467 95 4.595 299.3094 96 4.696 330.971 97 4.797 364.9326 98 4.898 401.2971 99 4.999 440.17distribution of Z Normal distribution

1.48672E-06 0.000579917 2.45094E-06 0.0008687 3.9995E-06 0.001284552 6.46025E-06 0.001874696 1.03291E-05 0.002699714 1.63472E-05 0.003835413 2.56093E-05 0.005374035 3.97118E-05 0.007424283 6.09553E-05 0.010109452 9.26132E-05 0.013562852 0.000139285 0.017919633 0.000207351 0.023304116 0.000305546 0.029811945 0.000445674 0.037486681 0.000643469 0.0462911 0.000919619 0.056074278 0.001300942 0.066536639 0.001821704 0.077196417 0.002525035 0.087362307 0.003464389 0.09611827 0.004704958 0.102327303 0.006324913 0.104661137 0.008416337 0.101662098 0.011085658 0.091841411 0.014453386 0.073814986 0.018652949 0.046473228 0.023828414 0.00917585 0.030130931 -0.03804338 0.03771375 -0.094282831 0.046725789 -0.1576157 0.057303789 -0.224997187 0.069563239 -0.292263436 0.083588399 -0.354244929 0.099421884 -0.405008262 0.117054396 -0.438227575 0.136415346 -0.447671321 0.157365126 -0.427773224 0.179689839 -0.374240219 0.203099244 -0.284637455 0.227228529 -0.158883344 

# 

#  

2 4 2 

## 336 6 24 z 

## z z   

    

     

#   2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z             

## ( ) z 0.251644341 0.000411873 0.275855243 0.18782147 0.299326439 0.395231257 0.321498297 0.612237125 0.341807853 0.8267965 0.359712192 1.026088455 0.37471238 1.197509618 0.386376486 1.329712319 0.394360216 1.413580947 0.398423793 1.443044227 0.398443914 1.415635461 0.394419966 1.33273831 0.386474058 1.199489353 0.374844865 1.024346204 0.359875719 0.818366595 0.34199778 0.594274668 0.32170943 0.365412073 0.299553264 0.144680625 0.276092166 -0.056420378 0.25188591 -0.228574626 0.227469632 -0.365184292 0.203335281 -0.462628185 0.17991684 -0.520241996 0.157579839 -0.540049159 0.136615273 -0.526293985 0.117237788 -0.484843542 0.099587708 -0.422530427 0.083736272 -0.346505441 0.069693339 -0.263658786 0.05741676 -0.180152901 0.046822635 -0.101092161 0.037795734 -0.030336761 0.030199481 0.029547598 0.023885038 0.07722465 0.018699163 0.112435203 0.014490659 0.135788687 0.011115369 0.148528978 0.008439746 0.152300952 0.006343145 0.148938347 0.004718997 0.140286733 0.003475077 0.128068772 0.002533081 0.113793105 0.001827693 0.098703708 0.001305351 0.083763503 0.000922829 0.0696644 0.00064578 0.0568556 0.00044732 0.045582551 0.000306705 0.035930124 0.000208159 0.0278651090.000139842 0.021274633 9.29928E-05 0.015998559 6.12113E-05 0.011855066 3.98826E-05 0.008659501 2.5722E-05 0.00623718 1.64209E-05 0.004431121 1.03767E-05 0.003105833 6.49066E-06 0.00214822 4.01874E-06 0.001466568 2.46298E-06 0.000988385 1.49417E-06 0.000657689Absolute values

0.000579917 2.92858E-05 0.0008687 8.77387E-05 0.001284552 0.00012974 0.001874696 0.000189344 0.002699714 0.000272671 0.003835413 0.000387377 0.005374035 0.000542778 0.007424283 0.000749853 0.010109452 0.001021055 0.013562852 0.001369848 0.017919633 0.001809883 0.023304116 0.002353716 0.029811945 0.003011006 0.037486681 0.003786155 0.0462911 0.004675401 0.056074278 0.005663502 0.066536639 0.006720201 0.077196417 0.007796838 0.087362307 0.008823593 0.09611827 0.009707945 0.102327303 0.010335058 0.104661137 0.010570775 0.101662098 0.010267872 0.091841411 0.009275983 0.073814986 0.007455314 0.046473228 0.004693796 0.00917585 0.000926761 0.03804338 0.003842381 0.094282831 0.009522566 0.1576157 0.015919186 0.224997187 0.022724716 0.292263436 0.029518607 0.354244929 0.035778738 0.405008262 0.040905835 0.438227575 0.044260985 0.447671321 0.045214803 0.427773224 0.043205096 0.374240219 0.037798262 0.284637455 0.028748383 0.158883344 0.016047218 

## 

#  

2 4 2 

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

       1 

## ( ) 2 () () 2 M i

i 

## xf a f x f b

 

##  

      

# 0.000411873 4.15991E-05 0.18782147 0.018969969 0.395231257 0.039918357 0.612237125 0.06183595 0.8267965 0.083506447 1.026088455 0.103634934 1.197509618 0.120948471 1.329712319 0.134300944 1.413580947 0.142771676 1.443044227 0.145747467 1.415635461 0.142979182 1.33273831 0.134606569 1.199489353 0.121148425 1.024346204 0.103458967 0.818366595 0.082655026 0.594274668 0.060021741 0.365412073 0.036906619 0.144680625 0.014612743 0.056420378 0.005698458 0.228574626 0.023086037 0.365184292 0.036883613 0.462628185 0.046725447 0.520241996 0.052544442 0.540049159 0.054544965 0.526293985 0.053155692 0.484843542 0.048969198 0.422530427 0.042675573 0.346505441 0.03499705 0.263658786 0.026629537 0.180152901 0.018195443 0.101092161 0.010210308 0.030336761 0.003064013 0.029547598 0.002984307 0.07722465 0.00779969 0.112435203 0.011355955 0.135788687 0.013714657 0.148528978 0.015001427 0.152300952 0.015382396 0.148938347 0.015042773 0.140286733 0.01416896 0.128068772 0.012934946 0.113793105 0.011493104 0.098703708 0.009969074 0.083763503 0.008460114 0.0696644 0.007036104 0.0568556 0.005742416 0.045582551 0.004603838 0.035930124 0.003628943 0.027865109 0.0028143760.021274633 0.002148738 0.015998559 0.001615854 0.011855066 0.001197362 0.008659501 0.00087461 0.00623718 0.000629955 0.004431121 0.000447543 0.003105833 0.000313689 0.00214822 0.00021697 0.001466568 0.000148123 0.000988385 9.98269E-05 0.000657689 3.32133E-05Cumulative normalization
2.92858E-05 1.10037E-05 0.000117025 4.39703E-05 0.000246764 9.27182E-05 0.000436108 0.000163862 0.00070878 0.000266314 0.001096156 0.000411865 0.001638934 0.000615806 0.002388786 0.000897553 0.003409841 0.0012812 0.004779689 0.001795901 0.006589572 0.002475939 0.008943288 0.003360314 0.011954294 0.004491657 0.015740449 0.005914251 0.02041585 0.007670967 0.026079352 0.009798948 0.032799553 0.012323968 0.040596391 0.01525352 0.049419984 0.01856886 0.059127929 0.022216484 0.069462986 0.026099735 0.080033761 0.030071555 0.090301633 0.033929562 0.099577616 0.037414882 0.107032929 0.04021611 0.111726725 0.041979738 0.112653486 0.042327955 0.116495868 0.043771676 0.126018434 0.047349645 0.141937619 0.053331054 0.164662335 0.061869545 0.194180942 0.072960745 0.22995968 0.0864041 0.270865514 0.101773889 0.3151265 0.118404328 0.360341303 0.135393152 0.403546399 0.151626856 0.441344661 0.165829018 0.470093044 0.176630817 0.486140262 0.182660332 

## ( ) 2 () () f a f x f b        0.486181861 0.182675963 0.505151829 0.18980366 0.545070186 0.204802419 0.606906136 0.228036403 0.690412582 0.25941277 0.794047516 0.298352131 0.914995988 0.34379681 1.049296932 0.394258492 1.192068608 0.447902931 1.337816075 0.502665482 1.480795256 0.556387888 1.615401825 0.606964404 1.73655025 0.652484212 1.840009217 0.691357457 1.922664243 0.722413915 1.982685984 0.744966236 2.019592604 0.758833376 2.034205347 0.764323908 2.039903805 0.766465023 2.062989842 0.775139275 2.099873456 0.788997772 2.146598902 0.806554198 2.199143344 0.826297029 2.253688309 0.846791529 2.306844002 0.866764029 2.355813199 0.885163513 2.398488772 0.901198257 2.433485822 0.914347903 2.460115359 0.924353576 2.478310802 0.931190256 2.488521111 0.935026635 2.491585124 0.936177895 2.494569431 0.937299206 2.502369121 0.940229829 2.513725076 0.944496669 2.527439734 0.949649758 2.54244116 0.955286332 2.557823556 0.96106605 2.572866329 0.966718159 2.58703529 0.972041945 2.599970236 0.976902069 2.611463339 0.98122044 2.621432414 0.984966179 2.629892527 0.988144947 2.636928632 0.990788664 2.642671047 0.992946295 2.647274885 0.994676122 2.650903828 0.996039646 2.653718204 0.9970971082.655866942 0.997904466 2.657482796 0.9985116 2.658680158 0.998961492 2.659554767 0.999290114 2.660184722 0.999526811 2.660632266 0.999694969 2.660945955 0.999812833 2.661162925 0.999894357 2.661311048 0.999950012 2.661410875 0.999987521 2.661444089 1 132.8984354Raw Data Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 n for each source 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sample size 0 KURTOSIS CALCULATIONS FOR SAMPLE SETS WITH n > 3 ONLY Testing Normality Raw Data Logtransformed Sample Size 0.00 0.00 Kurtosis #DIV/0! #DIV/0! http://www.spcforexcel.com/are-skewness-and-kurtosis-useful-statistics SE Kurtosis 0.00 0.00 note: cannot use this equation when n=3 because the denominator in second component is not defined (the term n-3 in denominator of second component is zero). Result Kurtosis #DIV/0! #DIV/0! Skewness #DIV/0! #DIV/0! SE Skewness 0.00 0.00 Result Raw Data Result Log Data Result Skewness #DIV/0! #DIV/0! #DIV/0! #DIV/0!
KURTOSIS CALCULATIONS FOR SAMPLE SETS WITH n = 3 ONLY Average #DIV/0! Standard Deviation #DIV/0! http://www.spiderfinancial.com/support/documentation/numxl/reference-manual/statistical-tests/test_xkurt

1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Testing Normality Raw Data Sample Size 0.00 Kurtosis -3.00 SE Kurtosis #DIV/0! Result Kurtosis #DIV/0! Skewness #DIV/0! SE Skewness 0.00 Result Raw Data Result Skewness #DIV/0! #DIV/0! ### The kurtosis and skewness are pulled into "Calculations for Template skew", in cells H12 and H14 respectively kurtosis= #DIV/0! depending on sample size skewness= #DIV/0! same for n>3 and n=3 ni = number test runs = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 0
n =Total # test runs = 0

1 N i df n  
    

###  1

N i in

  N

1 N i in

 -1

This step is for QC only:
means #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Mean = #DIV/0!

Pooled Variance = #DIV/0!

m= number future runs = 3
Term1 #DIV/0!

Term2 #DIV/0!

Squared root Term2 #DIV/0! NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = #NUM! UPL based on t-statistic with df at 99% confidence level #DIV/0!

0 #NUM!

#NUM! Current Confidence Level is Adjustment for non-normality (skewness and kurtosis) for any sample size in particular for small samples a) n = number of test-runs = b) Calculate u0 2 1 0 1 1 u t n 



###  2 2 1 11n i i s xX n   



###  1 1

1 i n N ij i j X x n   

### 

1 1 n m 

21 1 s n m        1 1 i i df n

       

### 

df t 21 1

sn m        1 1 i n i ik

k i x x n  

### Conclusion interval of differences for t-values used 0.103 3.982929999 Adjusted UPL based on recalculated t-statistic #DIV/0!

#NUM!

new t-statistic from tab Recalculate t-statisticLogtransformed

0 0 0 0 0 0 0 0 0 0 0 0 0 0

note: cannot use this equation when n=3 because the denominator in second component is not defined (the term n-3 in denominator of second component is zero).0 0 0 0 0 0 0 0 0 0 0 0 0 0#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3
c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6

c.1.7 #NUM! d.1.7 Calculations Calculations Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

## , x 

### I ab a a w a a

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

     

## ( ,)   ( ) w a e w  
a w  Result1: #NUM! Result2:

1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!

Result #DIV/0! 0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn  

#      

1 2 4 1 1 11 11 31 ( ) , , ,

n n n n n n n n P t I I I    

                  4-Calculate

4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! Corrected probability is:: 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          

3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       0.5 a= 1.5

0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6
#NUM! e.1.7 Calculations Calculations d.1.) Calculate e.1.) Calculate 

##   3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

     

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

    #NUM! Result3:



# 1 2 4 1 1 11 11 31 ( ) , , , n n n n P t I I I    

               #NUM! 0 0 0



# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I    

                     

1 1 1 1 72 2 2 24 2 2

3 1 5 1 24 2 2 72 2 2

      

                   a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!
#NUM! f.1.7 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

    #NUM! Result4: #NUM!a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3 g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6
g.1.7 #NUM! h.1.7 h.1.) Calculate

Calculations Calculations g.1.) Calculate 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

     

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        

2

### 3 1 2 6 w a  

    Result5: #NUM! Result6:#NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM!
#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a         3 1 2 6 w a  

    #NUM!#NUM! 0.103 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 4) If you don't get a YES in row 11, play around with the cell G3, the interval for differences until you get one p-value closed to 0.01 5) Once you get a YES, use the t-statistic in the calculations of the UPL. Go back to Template_nonnormal tab and paste the value in row 5 that has a Yes in row 11. Copy the new t-value in cell E164 of**Template_nonnormal n<3** 1) Start with initial t-statistic from Template 2) Determine interval of differences for t-values 2) Candidate values for t-statistic 3) Corrected p-values Acutal significance level with t-value 4) Is p-value closed enough to 0.01?t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3
c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2

5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3 g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3

c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3
g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3

c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3
g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3

c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3
g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3

c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3
g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    t-statistic=

Incomplete Beta Function approximation

where Inputs kurtosis= #DIV/0! x=u0= #NUM! skewness= #DIV/0!
n= 0 t0=t= #NUM!

a= -0.5 a= b= 0.5 b=
w= #NUM! w=

c.1.1. #NUM! d.1.1. c.1.2. #NUM! d.1.2. c.1.3 #NUM! d.1.3

c.1.4. #NUM! d.1.4. c.1.5. -1.5625 d.1.5.

c.1.6 #NUM! d.1.6 Calculations Calculations Calculate u0. Sustitute each candidate t-value in u0 equation

Calculate the Incomplete Beta Functions needed for adjustment

c.1.) Calculate d.1.) Calculate 

### 1x w b x    

   

##   , x 

### I ab a a w a a         

0 

### 1 1 , 2 2 u 

### n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b   2 

### 1 0 1 1 u t n 

c.1.7 #NUM! d.1.7

Result1: #NUM! Result2:
1- Calculate #NUM!

2- Calculate

2.1. Calculate #DIV/0!

2.2. Calculate #NUM!

2.3. Calculate #NUM!

Result: #DIV/0!

3-Calculate

3.1. Calculate #DIV/0!

3.2. Calculate #DIV/0!



### 2 6 3    

2

### 3 1 2 6 w a  

    

0 0 

### 1 11 ( ) , 2 2 2 u 

### n P t I 

      

3 0 0 

### 2 1 1 1 1 ( ) ,1 ,1

2 2 6 2 3 2

u u 

### n n n n P t I I

n n  

###  

         

        2 2 01 2 2 0 

### 2 1 1 1 1 ( ) 6 2 1 1 n



### n t n P t n t

n  

###  



###      

     

  

   

## 2 1 6 2 nn 

2

0 

## 2 1 1 1 n t n 

 1 2 2 0 

## 1 1 n 

## t n  

##     

  

1 3 2 nn  

## 2 1 6 2 nn Result #DIV/0!

4-Calculate
4.1. Calculate #NUM!

4.2. Calculate #DIV/0!

4.3. Calculate #DIV/0!

Result: #NUM!
5- Calculate

#NUM! 5.1. Calculate #DIV/0! 5.2. Calculate

5.3. Calculate #DIV/0!

5.4. Calculate #DIV/0!

Result #NUM! 

#      
4 0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u



# n n n n n n n n P t I I I n n  

#    

                        

0 

## 1 11

, 24 2 2 u 

## n n I         

#    0 

## 1 2 1 1

, 12 2 2

u 

## n n n

I n   

      

#    0 

### 4 1 3 1

, 24 2 2

u 

### n n n

I n   

      

#    

#    

#    

#   2 3/2 0 0

2 2

0 0



### 1 2 5 8 1 (2 5) 1 1 1 1 ( ) , ,

72 2 2 24 2 2 1 2 5 12 12 5 12 3 1 5 1 , , 24 2 2 72 2 2 u u

u u



### n n n n n n n P t I I n n n n n n n n n I I n n  

###   

   

      

                   

         

#   0 

## 1 (2 5) 1 1

, 72 2 2

u 

## n n n

I  



      

#  

#  

2 0 

## 1 2 5 8 1 1 , 24 2 2 u 

## n n n n

I n    

      

#  

#  

2 0 

## 1 2 5 12 3 1 , 24 2 2 u 

## n n n n

I n           

#  

#  

2 0 

## 1 2 5 12 5 1 , 72 2 2 u 

## n n n n

I n          Corrected probability is:: 3 4 3/2 2 0 3 

### ( ) ( ) ( ) ( ) P t SkewnessP t KurtosisP t P t    

###       #NUM! u0= #NUM!

0.5 a= 1.5 0.5 b= 0.5 #NUM! w= #NUM!

#NUM! e.1.1. #NUM! 1.772453851 e.1.2. 0.886226925 #NUM! e.1.3 #NUM!
#NUM! e.1.4. #NUM! 0.0625 e.1.5.

#NUM! e.1.6 Calculations e.1.) Calculate 

##  3 2 2 2

2 3 

### ( ,) 1 1 5 3 1 3 11 1 , ( ) ( ) 2 2 3 2 326 3 2 3 1 1 2 6 2 w a 

### a w e w a w a I ab a a w a a

a a b b

w a w  

###    



           

                        

0 1 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a 1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! e.1.7

#NUM! Result3: 

### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    0 0 0 

# 1 2 4 1 1 11 11 31 ( ) , , , 24 2 2 12 2 2 24 2 2 u u u 

# n n n n P t I I I                      #NUM!a= 1.5 b= 0.5
w= #NUM!

f.1.1. #NUM! f.1.2. 0.886226925 f.1.3 #NUM!
f.1.4. #NUM! -0.14583 f.1.5. -0.14583

#NUM! f.1.6 #NUM!

Calculations f.1.) Calculate 0 3 1 , 2 2 u n I        0 5 1 , 2 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        #NUM! f.1.7 #NUM!

#NUM! Result4: #NUM! 

### 2 6 3    

2

### 3 1 2 6 w a  

    a= -0.5 a= 0.5

b= 1 b= 1
w= #NUM! w= #NUM!

g.1.1. #NUM! h.1.1. g.1.2. #NUM! h.1.2. g.1.3 #NUM! h.1.3
g.1.4. #NUM! h.1.4. g.1.5. -1.5625 h.1.5.

g.1.6 #NUM! h.1.6 g.1.) Calculate h.1.) Calculate

Calculations Calculations 0 1,1 2 u n I       



## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a         

## ( ,) ( ) a  ( ) w a e w a  1 2 a w b  

3 2 5 3 1 2 3 2 3 a a a   

2 

### 3 11 1 2 6 3 w a a        g.1.7 #NUM! h.1.7

Result5: #NUM! Result6:



### 2 6 3    

2

### 3 1 2 6 w a  

     

### 2 6 3    

2

### 3 1 2 6 w a  

    #NUM!

1.772454 #NUM!
#NUM! 0.0625

#NUM! 0 1,1 2 u n I       

5 3 1 2 3 2 3 a a   

2 

### 3 11 1 2 6 3 w a a        #NUM!

#NUM! 

### 2 6 3     3 1 2 6 w a  

    